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OrderedCycle.tbl.md

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OrderedCycle

['A225479', 'A048594', 'A075181']

OrderedCycle Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, 1, 2]
Row3 [0, 2, 6, 6]
Row4 [0, 6, 22, 36, 24]
Row5 [0, 24, 100, 210, 240, 120]
Row6 [0, 120, 548, 1350, 2040, 1800, 720]
Row7 [0, 720, 3528, 9744, 17640, 21000, 15120, 5040]
Row8 [0, 5040, 26136, 78792, 162456, 235200, 231840, 141120, 40320]
Row9 [0, 40320, 219168, 708744, 1614816, 2693880, 3265920, 2751840, 1451520, 362880]

OrderedCycle Triangles

Flat Seq
Triangle [[1], [0, 1], [0, 1, 2], [0, 2, 6, 6], [0, 6, 22, 36, 24], [0, 24, 100, 210, 240, 120], [0, 120, 548, 1350, 2040, 1800, 720], [0, 720, 3528, 9744, 17640, 21000, 15120, 5040], [0, 5040, 26136, 78792, 162456, 235200, 231840, 141120, 40320], [0, 40320, 219168, 708744, 1614816, 2693880, 3265920, 2751840, 1451520, 362880]]
RevTabl [[1], [1, 0], [2, 1, 0], [6, 6, 2, 0], [24, 36, 22, 6, 0], [120, 240, 210, 100, 24, 0], [720, 1800, 2040, 1350, 548, 120, 0], [5040, 15120, 21000, 17640, 9744, 3528, 720, 0], [40320, 141120, 231840, 235200, 162456, 78792, 26136, 5040, 0], [362880, 1451520, 2751840, 3265920, 2693880, 1614816, 708744, 219168, 40320, 0]]
AntiDiag [[1], [0], [0, 1], [0, 1], [0, 2, 2], [0, 6, 6], [0, 24, 22, 6], [0, 120, 100, 36], [0, 720, 548, 210, 24], [0, 5040, 3528, 1350, 240]]
AccTabl [[1], [0, 1], [0, 1, 3], [0, 2, 8, 14], [0, 6, 28, 64, 88], [0, 24, 124, 334, 574, 694], [0, 120, 668, 2018, 4058, 5858, 6578], [0, 720, 4248, 13992, 31632, 52632, 67752, 72792], [0, 5040, 31176, 109968, 272424, 507624, 739464, 880584, 920904], [0, 40320, 259488, 968232, 2583048, 5276928, 8542848, 11294688, 12746208, 13109088]]
RevAccTabl [[1], [1, 0], [3, 1, 0], [14, 8, 2, 0], [88, 64, 28, 6, 0], [694, 574, 334, 124, 24, 0], [6578, 5858, 4058, 2018, 668, 120, 0], [72792, 67752, 52632, 31632, 13992, 4248, 720, 0], [920904, 880584, 739464, 507624, 272424, 109968, 31176, 5040, 0], [13109088, 12746208, 11294688, 8542848, 5276928, 2583048, 968232, 259488, 40320, 0]]
AccRevTabl [[1], [1, 1], [2, 3, 3], [6, 12, 14, 14], [24, 60, 82, 88, 88], [120, 360, 570, 670, 694, 694], [720, 2520, 4560, 5910, 6458, 6578, 6578], [5040, 20160, 41160, 58800, 68544, 72072, 72792, 72792], [40320, 181440, 413280, 648480, 810936, 889728, 915864, 920904, 920904], [362880, 1814400, 4566240, 7832160, 10526040, 12140856, 12849600, 13068768, 13109088, 13109088]]
DiffxTabl [[1], [0, 2], [0, 2, 6], [0, 4, 18, 24], [0, 12, 66, 144, 120], [0, 48, 300, 840, 1200, 720], [0, 240, 1644, 5400, 10200, 10800, 5040], [0, 1440, 10584, 38976, 88200, 126000, 105840, 40320], [0, 10080, 78408, 315168, 812280, 1411200, 1622880, 1128960, 362880], [0, 80640, 657504, 2834976, 8074080, 16163280, 22861440, 22014720, 13063680, 3628800]]

OrderedCycle Row sums

Trait Seq
RowSum [1, 1, 3, 14, 88, 694, 6578, 72792, 920904, 13109088]
EvenSum [1, 0, 2, 6, 46, 340, 3308, 36288, 460752, 6551424]
OddSum [0, 1, 1, 8, 42, 354, 3270, 36504, 460152, 6557664]
AltSum [1, -1, 1, -2, 4, -14, 38, -216, 600, -6240]
AbsSum [1, 1, 3, 14, 88, 694, 6578, 72792, 920904, 13109088]
AccSum [1, 1, 4, 24, 186, 1750, 19300, 243768, 3467184, 54820848]
AccRevSum [1, 2, 8, 46, 342, 3108, 33324, 411360, 5741856, 89379120]
DiagSum [1, 0, 1, 1, 4, 12, 52, 256, 1502, 10158]

OrderedCycle Transforms

Trans Seq
RowLcm [1, 1, 2, 6, 792, 8400, 25153200, 76734000, 763351047043200, 2541777015532656545280]
RowGcd [1, 1, 2, 2, 2, 2, 2, 24, 24, 24]
RowMax [1, 1, 2, 6, 36, 240, 2040, 21000, 235200, 3265920]
CentralE [1, 1, 22, 1350, 162456]
CentralO [0, 2, 100, 9744, 1614816]
ColMiddle [1, 0, 1, 2, 22, 100, 1350, 9744, 162456, 1614816]
ColLeft [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
BinConv [1, 1, 4, 30, 324, 4540, 78060, 1589448, 37388400, 997513200]
InvBinConv [1, 1, 0, -6, -12, 140, 1020, -5208, -117264, -2448]
TransSqrs [0, 1, 9, 80, 802, 9154, 118022, 1701048, 27139608, 475183584]
TransNat0 [0, 1, 5, 32, 254, 2414, 26746, 338568, 4820952, 76270032]
TransNat1 [1, 2, 8, 46, 342, 3108, 33324, 411360, 5741856, 89379120]
PosHalf [1, 1, 4, 26, 232, 2624, 35888, 575280, 10569984, 218911872]
NegHalf [1, 1, 0, 2, -8, 64, -592, 6768, -90624, 1395840]

OrderedCycle Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
DiagRow1 [0, 1, 6, 36, 240, 1800, 15120, 141120, 1451520, 16329600]
DiagRow2 [0, 2, 22, 210, 2040, 21000, 231840, 2751840, 35078400, 479001600]
DiagRow3 [0, 6, 100, 1350, 17640, 235200, 3265920, 47628000, 731808000, 11855289600]
DiagRow4 [0, 24, 548, 9744, 162456, 2693880, 45556560, 795175920, 14411295360, 271965133440]
DiagRow5 [0, 120, 3528, 78792, 1614816, 32319000, 649479600, 13293292320, 279281882880, 6049083680640]
DiagRow6 [0, 720, 26136, 708744, 17368320, 410031600, 9604465200, 226750764240, 5444670591360, 133689206851200]
DiagRow7 [0, 5040, 219168, 7036200, 201828000, 5519487600, 148370508000, 3986353491120, 108116216208000, 2978384048640000]
DiagRow8 [0, 40320, 2053152, 76521456, 2526193824, 78864820320, 2402005525920, 72622987557120, 2202727143576960, 67478689070432640]
DiagRow9 [0, 362880, 21257280, 905507856, 33936357312, 1194924450720, 40797624067200, 1374928181827200, 46243059751848960, 1563325251963995520]

OrderedCycle Diagonals as columns

DiagCol Seq
DiagCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
DiagCol2 [2, 6, 22, 100, 548, 3528, 26136, 219168, 2053152, 21257280]
DiagCol3 [6, 36, 210, 1350, 9744, 78792, 708744, 7036200, 76521456, 905507856]
DiagCol4 [24, 240, 2040, 17640, 162456, 1614816, 17368320, 201828000, 2526193824, 33936357312]
DiagCol5 [120, 1800, 21000, 235200, 2693880, 32319000, 410031600, 5519487600, 78864820320, 1194924450720]
DiagCol6 [720, 15120, 231840, 3265920, 45556560, 649479600, 9604465200, 148370508000, 2402005525920, 40797624067200]
DiagCol7 [5040, 141120, 2751840, 47628000, 795175920, 13293292320, 226750764240, 3986353491120, 72622987557120, 1374928181827200]
DiagCol8 [40320, 1451520, 35078400, 731808000, 14411295360, 279281882880, 5444670591360, 108116216208000, 2202727143576960, 46243059751848960]
DiagCol9 [362880, 16329600, 479001600, 11855289600, 271965133440, 6049083680640, 133689206851200, 2978384048640000, 67478689070432640, 1563325251963995520]

OrderedCycle Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow2 [0, 3, 10, 21, 36, 55, 78, 105, 136, 171]
PolyRow3 [0, 14, 76, 222, 488, 910, 1524, 2366, 3472, 4878]
PolyRow4 [0, 88, 772, 3132, 8824, 20080, 39708, 71092, 118192, 185544]
PolyRow5 [0, 694, 9808, 55242, 199456, 553870, 1293264, 2670178, 5029312, 8821926]
PolyRow6 [0, 6578, 149552, 1169262, 5410208, 18333050, 50545008, 120348662, 256809152, 503339778]
PolyRow7 [0, 72792, 2660544, 28873800, 171209664, 707959800, 2304709632, 6328330344, 15298865280, 33504712344]
PolyRow8 [0, 920904, 54093696, 814870584, 6192052800, 31244562600, 120100860864, 380302313496, 1041597412224, 2548839457800]
PolyRow9 [0, 13109088, 1237306560, 25871762016, 251937937920, 1551289408800, 7040906019648, 25711138981920, 79779826369536, 218138133235680]

OrderedCycle Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, 3, 14, 88, 694, 6578, 72792, 920904, 13109088]
PolyCol2 [1, 2, 10, 76, 772, 9808, 149552, 2660544, 54093696, 1237306560]
PolyCol3 [1, 3, 21, 222, 3132, 55242, 1169262, 28873800, 814870584, 25871762016]
PolyCol4 [1, 4, 36, 488, 8824, 199456, 5410208, 171209664, 6192052800, 251937937920]
PolyCol5 [1, 5, 55, 910, 20080, 553870, 18333050, 707959800, 31244562600, 1551289408800]
PolyCol6 [1, 6, 78, 1524, 39708, 1293264, 50545008, 2304709632, 120100860864, 7040906019648]
PolyCol7 [1, 7, 105, 2366, 71092, 2670178, 120348662, 6328330344, 380302313496, 25711138981920]
PolyCol8 [1, 8, 136, 3472, 118192, 5029312, 256809152, 15298865280, 1041597412224, 79779826369536]
PolyCol9 [1, 9, 171, 4878, 185544, 8821926, 503339778, 33504712344, 2548839457800, 218138133235680]

OrderedCycle:Rev

[]

OrderedCycle:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [2, 1, 0]
Row3 [6, 6, 2, 0]
Row4 [24, 36, 22, 6, 0]
Row5 [120, 240, 210, 100, 24, 0]
Row6 [720, 1800, 2040, 1350, 548, 120, 0]
Row7 [5040, 15120, 21000, 17640, 9744, 3528, 720, 0]
Row8 [40320, 141120, 231840, 235200, 162456, 78792, 26136, 5040, 0]
Row9 [362880, 1451520, 2751840, 3265920, 2693880, 1614816, 708744, 219168, 40320, 0]

OrderedCycle:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [2, 1, 0], [6, 6, 2, 0], [24, 36, 22, 6, 0], [120, 240, 210, 100, 24, 0], [720, 1800, 2040, 1350, 548, 120, 0], [5040, 15120, 21000, 17640, 9744, 3528, 720, 0], [40320, 141120, 231840, 235200, 162456, 78792, 26136, 5040, 0], [362880, 1451520, 2751840, 3265920, 2693880, 1614816, 708744, 219168, 40320, 0]]
RevTabl [[1], [0, 1], [0, 1, 2], [0, 2, 6, 6], [0, 6, 22, 36, 24], [0, 24, 100, 210, 240, 120], [0, 120, 548, 1350, 2040, 1800, 720], [0, 720, 3528, 9744, 17640, 21000, 15120, 5040], [0, 5040, 26136, 78792, 162456, 235200, 231840, 141120, 40320], [0, 40320, 219168, 708744, 1614816, 2693880, 3265920, 2751840, 1451520, 362880]]
AntiDiag [[1], [1], [2, 0], [6, 1], [24, 6, 0], [120, 36, 2], [720, 240, 22, 0], [5040, 1800, 210, 6], [40320, 15120, 2040, 100, 0], [362880, 141120, 21000, 1350, 24]]
AccTabl [[1], [1, 1], [2, 3, 3], [6, 12, 14, 14], [24, 60, 82, 88, 88], [120, 360, 570, 670, 694, 694], [720, 2520, 4560, 5910, 6458, 6578, 6578], [5040, 20160, 41160, 58800, 68544, 72072, 72792, 72792], [40320, 181440, 413280, 648480, 810936, 889728, 915864, 920904, 920904], [362880, 1814400, 4566240, 7832160, 10526040, 12140856, 12849600, 13068768, 13109088, 13109088]]
RevAccTabl [[1], [1, 1], [3, 3, 2], [14, 14, 12, 6], [88, 88, 82, 60, 24], [694, 694, 670, 570, 360, 120], [6578, 6578, 6458, 5910, 4560, 2520, 720], [72792, 72792, 72072, 68544, 58800, 41160, 20160, 5040], [920904, 920904, 915864, 889728, 810936, 648480, 413280, 181440, 40320], [13109088, 13109088, 13068768, 12849600, 12140856, 10526040, 7832160, 4566240, 1814400, 362880]]
AccRevTabl [[1], [0, 1], [0, 1, 3], [0, 2, 8, 14], [0, 6, 28, 64, 88], [0, 24, 124, 334, 574, 694], [0, 120, 668, 2018, 4058, 5858, 6578], [0, 720, 4248, 13992, 31632, 52632, 67752, 72792], [0, 5040, 31176, 109968, 272424, 507624, 739464, 880584, 920904], [0, 40320, 259488, 968232, 2583048, 5276928, 8542848, 11294688, 12746208, 13109088]]
DiffxTabl [[1], [1, 0], [2, 2, 0], [6, 12, 6, 0], [24, 72, 66, 24, 0], [120, 480, 630, 400, 120, 0], [720, 3600, 6120, 5400, 2740, 720, 0], [5040, 30240, 63000, 70560, 48720, 21168, 5040, 0], [40320, 282240, 695520, 940800, 812280, 472752, 182952, 40320, 0], [362880, 2903040, 8255520, 13063680, 13469400, 9688896, 4961208, 1753344, 362880, 0]]

OrderedCycle:Rev Row sums

Trait Seq
RowSum [1, 1, 3, 14, 88, 694, 6578, 72792, 920904, 13109088]
EvenSum [1, 1, 2, 8, 46, 354, 3308, 36504, 460752, 6557664]
OddSum [0, 0, 1, 6, 42, 340, 3270, 36288, 460152, 6551424]
AltSum [1, 1, 1, 2, 4, 14, 38, 216, 600, 6240]
AbsSum [1, 1, 3, 14, 88, 694, 6578, 72792, 920904, 13109088]
AccSum [1, 2, 8, 46, 342, 3108, 33324, 411360, 5741856, 89379120]
AccRevSum [1, 1, 4, 24, 186, 1750, 19300, 243768, 3467184, 54820848]
DiagSum [1, 1, 2, 7, 30, 158, 982, 7056, 57580, 526374]

OrderedCycle:Rev Transforms

Trans Seq
RowLcm [1, 1, 2, 6, 792, 8400, 25153200, 76734000, 763351047043200, 2541777015532656545280]
RowGcd [1, 1, 2, 2, 2, 2, 2, 24, 24, 24]
RowMax [1, 1, 2, 6, 36, 240, 2040, 21000, 235200, 3265920]
CentralE [1, 1, 22, 1350, 162456]
CentralO [1, 6, 210, 17640, 2693880]
ColMiddle [1, 1, 1, 6, 22, 210, 1350, 17640, 162456, 2693880]
ColLeft [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
ColRight [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv [1, 1, 4, 30, 324, 4540, 78060, 1589448, 37388400, 997513200]
InvBinConv [1, -1, 0, 6, -12, -140, 1020, 5208, -117264, 2448]
TransSqrs [0, 0, 1, 14, 178, 2364, 33878, 527904, 8942232, 164159136]
TransNat0 [0, 0, 1, 10, 98, 1056, 12722, 170976, 2546280, 41711760]
TransNat1 [1, 1, 4, 24, 186, 1750, 19300, 243768, 3467184, 54820848]
PosHalf [1, 2, 10, 76, 772, 9808, 149552, 2660544, 54093696, 1237306560]
NegHalf [1, -2, 6, -28, 172, -1328, 12272, -132480, 1633344, -22663104]

OrderedCycle:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
DiagRow2 [2, 6, 22, 100, 548, 3528, 26136, 219168, 2053152, 21257280]
DiagRow3 [6, 36, 210, 1350, 9744, 78792, 708744, 7036200, 76521456, 905507856]
DiagRow4 [24, 240, 2040, 17640, 162456, 1614816, 17368320, 201828000, 2526193824, 33936357312]
DiagRow5 [120, 1800, 21000, 235200, 2693880, 32319000, 410031600, 5519487600, 78864820320, 1194924450720]
DiagRow6 [720, 15120, 231840, 3265920, 45556560, 649479600, 9604465200, 148370508000, 2402005525920, 40797624067200]
DiagRow7 [5040, 141120, 2751840, 47628000, 795175920, 13293292320, 226750764240, 3986353491120, 72622987557120, 1374928181827200]
DiagRow8 [40320, 1451520, 35078400, 731808000, 14411295360, 279281882880, 5444670591360, 108116216208000, 2202727143576960, 46243059751848960]
DiagRow9 [362880, 16329600, 479001600, 11855289600, 271965133440, 6049083680640, 133689206851200, 2978384048640000, 67478689070432640, 1563325251963995520]

OrderedCycle:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
DiagCol1 [0, 1, 6, 36, 240, 1800, 15120, 141120, 1451520, 16329600]
DiagCol2 [0, 2, 22, 210, 2040, 21000, 231840, 2751840, 35078400, 479001600]
DiagCol3 [0, 6, 100, 1350, 17640, 235200, 3265920, 47628000, 731808000, 11855289600]
DiagCol4 [0, 24, 548, 9744, 162456, 2693880, 45556560, 795175920, 14411295360, 271965133440]
DiagCol5 [0, 120, 3528, 78792, 1614816, 32319000, 649479600, 13293292320, 279281882880, 6049083680640]
DiagCol6 [0, 720, 26136, 708744, 17368320, 410031600, 9604465200, 226750764240, 5444670591360, 133689206851200]
DiagCol7 [0, 5040, 219168, 7036200, 201828000, 5519487600, 148370508000, 3986353491120, 108116216208000, 2978384048640000]
DiagCol8 [0, 40320, 2053152, 76521456, 2526193824, 78864820320, 2402005525920, 72622987557120, 2202727143576960, 67478689070432640]
DiagCol9 [0, 362880, 21257280, 905507856, 33936357312, 1194924450720, 40797624067200, 1374928181827200, 46243059751848960, 1563325251963995520]

OrderedCycle:Rev Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow2 [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
PolyRow3 [6, 14, 26, 42, 62, 86, 114, 146, 182, 222]
PolyRow4 [24, 88, 232, 492, 904, 1504, 2328, 3412, 4792, 6504]
PolyRow5 [120, 694, 2624, 7374, 16984, 34070, 61824, 104014, 164984, 249654]
PolyRow6 [720, 6578, 35888, 134478, 390128, 946970, 2019888, 3908918, 7013648, 11847618]
PolyRow7 [5040, 72792, 575280, 2887128, 10586736, 31175640, 78316272, 174588120, 354762288, 669594456]
PolyRow8 [40320, 920904, 10569984, 71281656, 331267200, 1185826920, 3513544704, 9032906904, 20804747136, 43905918600]
PolyRow9 [362880, 13109088, 218911872, 1988802720, 11738697600, 51161256480, 179003945088, 531187864032, 1387687612800, 3276218158560]

OrderedCycle:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
PolyCol1 [1, 1, 3, 14, 88, 694, 6578, 72792, 920904, 13109088]
PolyCol2 [1, 1, 4, 26, 232, 2624, 35888, 575280, 10569984, 218911872]
PolyCol3 [1, 1, 5, 42, 492, 7374, 134478, 2887128, 71281656, 1988802720]
PolyCol4 [1, 1, 6, 62, 904, 16984, 390128, 10586736, 331267200, 11738697600]
PolyCol5 [1, 1, 7, 86, 1504, 34070, 946970, 31175640, 1185826920, 51161256480]
PolyCol6 [1, 1, 8, 114, 2328, 61824, 2019888, 78316272, 3513544704, 179003945088]
PolyCol7 [1, 1, 9, 146, 3412, 104014, 3908918, 174588120, 9032906904, 531187864032]
PolyCol8 [1, 1, 10, 182, 4792, 164984, 7013648, 354762288, 20804747136, 1387687612800]
PolyCol9 [1, 1, 11, 222, 6504, 249654, 11847618, 669594456, 43905918600, 3276218158560]