Skip to content

Latest commit

 

History

History
246 lines (212 loc) · 10.9 KB

Euclid.tbl.md

File metadata and controls

246 lines (212 loc) · 10.9 KB
Raw

Euclid

['A217831']

Euclid Triangle view

Row Seq
Row0 [0]
Row1 [1, 1]
Row2 [0, 1, 0]
Row3 [0, 1, 1, 0]
Row4 [0, 1, 0, 1, 0]
Row5 [0, 1, 1, 1, 1, 0]
Row6 [0, 1, 0, 0, 0, 1, 0]
Row7 [0, 1, 1, 1, 1, 1, 1, 0]
Row8 [0, 1, 0, 1, 0, 1, 0, 1, 0]
Row9 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]

Euclid Triangles

Flat Seq
Triangle [[0], [1, 1], [0, 1, 0], [0, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]]
RevTabl [[0], [1, 1], [0, 1, 0], [0, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]]
AntiDiag [[0], [1], [0, 1], [0, 1], [0, 1, 0], [0, 1, 1], [0, 1, 0, 0], [0, 1, 1, 1], [0, 1, 0, 1, 0], [0, 1, 1, 0, 1]]
AccTabl [[0], [1, 2], [0, 1, 1], [0, 1, 2, 2], [0, 1, 1, 2, 2], [0, 1, 2, 3, 4, 4], [0, 1, 1, 1, 1, 2, 2], [0, 1, 2, 3, 4, 5, 6, 6], [0, 1, 1, 2, 2, 3, 3, 4, 4], [0, 1, 2, 2, 3, 4, 4, 5, 6, 6]]
RevAccTabl [[0], [2, 1], [1, 1, 0], [2, 2, 1, 0], [2, 2, 1, 1, 0], [4, 4, 3, 2, 1, 0], [2, 2, 1, 1, 1, 1, 0], [6, 6, 5, 4, 3, 2, 1, 0], [4, 4, 3, 3, 2, 2, 1, 1, 0], [6, 6, 5, 4, 4, 3, 2, 2, 1, 0]]
AccRevTabl [[0], [1, 2], [0, 1, 1], [0, 1, 2, 2], [0, 1, 1, 2, 2], [0, 1, 2, 3, 4, 4], [0, 1, 1, 1, 1, 2, 2], [0, 1, 2, 3, 4, 5, 6, 6], [0, 1, 1, 2, 2, 3, 3, 4, 4], [0, 1, 2, 2, 3, 4, 4, 5, 6, 6]]
DiffxTabl [[0], [1, 2], [0, 2, 0], [0, 2, 3, 0], [0, 2, 0, 4, 0], [0, 2, 3, 4, 5, 0], [0, 2, 0, 0, 0, 6, 0], [0, 2, 3, 4, 5, 6, 7, 0], [0, 2, 0, 4, 0, 6, 0, 8, 0], [0, 2, 3, 0, 5, 6, 0, 8, 9, 0]]

Euclid Row sums

Trait Seq
RowSum [0, 2, 1, 2, 2, 4, 2, 6, 4, 6]
EvenSum [0, 1, 0, 1, 0, 2, 0, 3, 0, 3]
OddSum [0, 1, 1, 1, 2, 2, 2, 3, 4, 3]
AltSum [0, 0, -1, 0, -2, 0, -2, 0, -4, 0]
AbsSum [0, 2, 1, 2, 2, 4, 2, 6, 4, 6]
AccSum [0, 3, 2, 5, 6, 14, 8, 27, 20, 33]
AccRevSum [0, 3, 2, 5, 6, 14, 8, 27, 20, 33]
DiagSum [0, 1, 1, 1, 1, 2, 1, 3, 2, 3]

Euclid Transforms

Trans Seq
RowLcm [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
RowGcd [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
RowMax [0, 1, 1, 1, 1, 1, 1, 1, 1, 1]
CentralE [0, 1, 0, 0, 0]
CentralO [1, 1, 1, 1, 1]
ColMiddle [0, 1, 1, 1, 0, 1, 0, 1, 0, 1]
ColLeft [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv [0, 2, 2, 6, 8, 30, 12, 126, 128, 342]
InvBinConv [0, 0, -2, 0, -8, 0, -12, 0, -128, 0]
TransSqrs [0, 1, 1, 5, 10, 30, 26, 91, 84, 159]
TransNat0 [0, 1, 1, 3, 4, 10, 6, 21, 16, 27]
TransNat1 [0, 3, 2, 5, 6, 14, 8, 27, 20, 33]
PosHalf [0, 3, 2, 6, 10, 30, 34, 126, 170, 438]
NegHalf [0, -1, -2, 2, -10, 10, -34, 42, -170, 114]

Euclid Diagonals as rows

DiagRow Seq
DiagRow0 [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow2 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagRow3 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]
DiagRow4 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagRow5 [0, 1, 1, 1, 1, 0, 1, 1, 1, 1]
DiagRow6 [0, 1, 0, 0, 0, 1, 0, 1, 0, 0]
DiagRow7 [0, 1, 1, 1, 1, 1, 1, 0, 1, 1]
DiagRow8 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagRow9 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]

Euclid Diagonals as columns

DiagCol Seq
DiagCol0 [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol2 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagCol3 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]
DiagCol4 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagCol5 [0, 1, 1, 1, 1, 0, 1, 1, 1, 1]
DiagCol6 [0, 1, 0, 0, 0, 1, 0, 1, 0, 0]
DiagCol7 [0, 1, 1, 1, 1, 1, 1, 0, 1, 1]
DiagCol8 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagCol9 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]

Euclid Polynomial values as rows

PolyRow Seq
PolyRow0 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyRow1 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
PolyRow2 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow3 [0, 2, 6, 12, 20, 30, 42, 56, 72, 90]
PolyRow4 [0, 2, 10, 30, 68, 130, 222, 350, 520, 738]
PolyRow5 [0, 4, 30, 120, 340, 780, 1554, 2800, 4680, 7380]
PolyRow6 [0, 2, 34, 246, 1028, 3130, 7782, 16814, 32776, 59058]
PolyRow7 [0, 6, 126, 1092, 5460, 19530, 55986, 137256, 299592, 597870]
PolyRow8 [0, 4, 170, 2460, 17476, 81380, 287934, 840700, 2130440, 4842756]
PolyRow9 [0, 6, 438, 9084, 83220, 472530, 1968666, 6607608, 18911304, 47895390]

Euclid Polynomial values as columns

PolyCol Seq
PolyCol0 [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [0, 2, 1, 2, 2, 4, 2, 6, 4, 6]
PolyCol2 [0, 3, 2, 6, 10, 30, 34, 126, 170, 438]
PolyCol3 [0, 4, 3, 12, 30, 120, 246, 1092, 2460, 9084]
PolyCol4 [0, 5, 4, 20, 68, 340, 1028, 5460, 17476, 83220]
PolyCol5 [0, 6, 5, 30, 130, 780, 3130, 19530, 81380, 472530]
PolyCol6 [0, 7, 6, 42, 222, 1554, 7782, 55986, 287934, 1968666]
PolyCol7 [0, 8, 7, 56, 350, 2800, 16814, 137256, 840700, 6607608]
PolyCol8 [0, 9, 8, 72, 520, 4680, 32776, 299592, 2130440, 18911304]
PolyCol9 [0, 10, 9, 90, 738, 7380, 59058, 597870, 4842756, 47895390]

Euclid:Rev

[]

Euclid:Rev Triangle view

Row Seq
Row0 [0]
Row1 [1, 1]
Row2 [0, 1, 0]
Row3 [0, 1, 1, 0]
Row4 [0, 1, 0, 1, 0]
Row5 [0, 1, 1, 1, 1, 0]
Row6 [0, 1, 0, 0, 0, 1, 0]
Row7 [0, 1, 1, 1, 1, 1, 1, 0]
Row8 [0, 1, 0, 1, 0, 1, 0, 1, 0]
Row9 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]

Euclid:Rev Triangles

Flat Seq
Triangle [[0], [1, 1], [0, 1, 0], [0, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]]
RevTabl [[0], [1, 1], [0, 1, 0], [0, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]]
AntiDiag [[0], [1], [0, 1], [0, 1], [0, 1, 0], [0, 1, 1], [0, 1, 0, 0], [0, 1, 1, 1], [0, 1, 0, 1, 0], [0, 1, 1, 0, 1]]
AccTabl [[0], [1, 2], [0, 1, 1], [0, 1, 2, 2], [0, 1, 1, 2, 2], [0, 1, 2, 3, 4, 4], [0, 1, 1, 1, 1, 2, 2], [0, 1, 2, 3, 4, 5, 6, 6], [0, 1, 1, 2, 2, 3, 3, 4, 4], [0, 1, 2, 2, 3, 4, 4, 5, 6, 6]]
RevAccTabl [[0], [2, 1], [1, 1, 0], [2, 2, 1, 0], [2, 2, 1, 1, 0], [4, 4, 3, 2, 1, 0], [2, 2, 1, 1, 1, 1, 0], [6, 6, 5, 4, 3, 2, 1, 0], [4, 4, 3, 3, 2, 2, 1, 1, 0], [6, 6, 5, 4, 4, 3, 2, 2, 1, 0]]
AccRevTabl [[0], [1, 2], [0, 1, 1], [0, 1, 2, 2], [0, 1, 1, 2, 2], [0, 1, 2, 3, 4, 4], [0, 1, 1, 1, 1, 2, 2], [0, 1, 2, 3, 4, 5, 6, 6], [0, 1, 1, 2, 2, 3, 3, 4, 4], [0, 1, 2, 2, 3, 4, 4, 5, 6, 6]]
DiffxTabl [[0], [1, 2], [0, 2, 0], [0, 2, 3, 0], [0, 2, 0, 4, 0], [0, 2, 3, 4, 5, 0], [0, 2, 0, 0, 0, 6, 0], [0, 2, 3, 4, 5, 6, 7, 0], [0, 2, 0, 4, 0, 6, 0, 8, 0], [0, 2, 3, 0, 5, 6, 0, 8, 9, 0]]

Euclid:Rev Row sums

Trait Seq
RowSum [0, 2, 1, 2, 2, 4, 2, 6, 4, 6]
EvenSum [0, 1, 0, 1, 0, 2, 0, 3, 0, 3]
OddSum [0, 1, 1, 1, 2, 2, 2, 3, 4, 3]
AltSum [0, 0, -1, 0, -2, 0, -2, 0, -4, 0]
AbsSum [0, 2, 1, 2, 2, 4, 2, 6, 4, 6]
AccSum [0, 3, 2, 5, 6, 14, 8, 27, 20, 33]
AccRevSum [0, 3, 2, 5, 6, 14, 8, 27, 20, 33]
DiagSum [0, 1, 1, 1, 1, 2, 1, 3, 2, 3]

Euclid:Rev Transforms

Trans Seq
RowLcm [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
RowGcd [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
RowMax [0, 1, 1, 1, 1, 1, 1, 1, 1, 1]
CentralE [0, 1, 0, 0, 0]
CentralO [1, 1, 1, 1, 1]
ColMiddle [0, 1, 1, 1, 0, 1, 0, 1, 0, 1]
ColLeft [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv [0, 2, 2, 6, 8, 30, 12, 126, 128, 342]
InvBinConv [0, 0, -2, 0, -8, 0, -12, 0, -128, 0]
TransSqrs [0, 1, 1, 5, 10, 30, 26, 91, 84, 159]
TransNat0 [0, 1, 1, 3, 4, 10, 6, 21, 16, 27]
TransNat1 [0, 3, 2, 5, 6, 14, 8, 27, 20, 33]
PosHalf [0, 3, 2, 6, 10, 30, 34, 126, 170, 438]
NegHalf [0, -1, -2, 2, -10, 10, -34, 42, -170, 114]

Euclid:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow2 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagRow3 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]
DiagRow4 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagRow5 [0, 1, 1, 1, 1, 0, 1, 1, 1, 1]
DiagRow6 [0, 1, 0, 0, 0, 1, 0, 1, 0, 0]
DiagRow7 [0, 1, 1, 1, 1, 1, 1, 0, 1, 1]
DiagRow8 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagRow9 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]

Euclid:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol2 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagCol3 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]
DiagCol4 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagCol5 [0, 1, 1, 1, 1, 0, 1, 1, 1, 1]
DiagCol6 [0, 1, 0, 0, 0, 1, 0, 1, 0, 0]
DiagCol7 [0, 1, 1, 1, 1, 1, 1, 0, 1, 1]
DiagCol8 [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
DiagCol9 [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]

Euclid:Rev Polynomial values as rows

PolyRow Seq
PolyRow0 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyRow1 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
PolyRow2 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow3 [0, 2, 6, 12, 20, 30, 42, 56, 72, 90]
PolyRow4 [0, 2, 10, 30, 68, 130, 222, 350, 520, 738]
PolyRow5 [0, 4, 30, 120, 340, 780, 1554, 2800, 4680, 7380]
PolyRow6 [0, 2, 34, 246, 1028, 3130, 7782, 16814, 32776, 59058]
PolyRow7 [0, 6, 126, 1092, 5460, 19530, 55986, 137256, 299592, 597870]
PolyRow8 [0, 4, 170, 2460, 17476, 81380, 287934, 840700, 2130440, 4842756]
PolyRow9 [0, 6, 438, 9084, 83220, 472530, 1968666, 6607608, 18911304, 47895390]

Euclid:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [0, 2, 1, 2, 2, 4, 2, 6, 4, 6]
PolyCol2 [0, 3, 2, 6, 10, 30, 34, 126, 170, 438]
PolyCol3 [0, 4, 3, 12, 30, 120, 246, 1092, 2460, 9084]
PolyCol4 [0, 5, 4, 20, 68, 340, 1028, 5460, 17476, 83220]
PolyCol5 [0, 6, 5, 30, 130, 780, 3130, 19530, 81380, 472530]
PolyCol6 [0, 7, 6, 42, 222, 1554, 7782, 55986, 287934, 1968666]
PolyCol7 [0, 8, 7, 56, 350, 2800, 16814, 137256, 840700, 6607608]
PolyCol8 [0, 9, 8, 72, 520, 4680, 32776, 299592, 2130440, 18911304]
PolyCol9 [0, 10, 9, 90, 738, 7380, 59058, 597870, 4842756, 47895390]