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Trinomial.md

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<style> table, td, th {border-collapse: collapse; font-family: sans-serif; color: blue;}
td, th {border-bottom: 0; padding: 4px}
tr:nth-child(odd) {background: #eee;}
tr:nth-child(even) {background: #fff;}
tr.header {background: orange !important; color: white; font-weight: bold;}
tr.subheader {background: lightgray !important; color: black;}
tr.headerLastRow {border-bottom: 2px solid black;}
th.rowNumber, td.rowNumber {text-align: right;} </style><body>
<table>
  <tr class = "header headerLastRow">
    <th style = "text-align: left;">Trait</th>
    <th style = "text-align: left;">ANumber</th>
    <th style = "text-align: left;">Sequence</th>
  </tr>
  <tr>
    <td style = "text-align: left;">Trinomial</td>
    <td style = "text-align: left;"></td>
    <td style = "text-align: left;"></td>
  </tr>
  <tr>
    <td style = "text-align: left;">Triangle</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A111808'>A111808</a></td>
    <td style = "text-align: left;">[1 1 1 1 2 3 1 3 6 7 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">Reverse</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A094531'>A094531</a></td>
    <td style = "text-align: left;">[1 1 1 3 2 1 7 6 3 1 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">InvRev</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A102587'>A102587</a></td>
    <td style = "text-align: left;">[1 -1 1 -1 -2 1 2 0 -3 1 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">DiagTri</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 1 1 1 1 2 1 3 3 1 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 1 1 1 1 2 1 3 3 1 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">PolyTri</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 1 1 1 2 1 1 6 3 1 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 1 1 1 2 1 1 6 3 1 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">Sum</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A027914'>A027914</a></td>
    <td style = "text-align: left;">[1 2 6 17 50 147 435 1290 3834 11411 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">EvenSum</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 1 4 7 30 61 253 547 2194 4921 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 1 4 7 30 61 253 547 2194 4921 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">OddSum</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[0 1 2 10 20 86 182 743 1640 6490 ]'>nomatch</a></td>
    <td style = "text-align: left;">[0 1 2 10 20 86 182 743 1640 6490 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">AltSum</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A246437'>A246437</a></td>
    <td style = "text-align: left;">[1 0 2 -3 10 -25 71 -196 554 -1569 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">DiagSum</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 1 2 3 7 11 23 38 78 132 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 1 2 3 7 11 23 38 78 132 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">Middle</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A027913'>A027913</a></td>
    <td style = "text-align: left;">[1 1 2 3 10 15 50 77 266 414 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">Central</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A027908'>A027908</a></td>
    <td style = "text-align: left;">[1 2 10 50 266 1452 8074 45474 258570 1481108 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">LeftSide</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A000012'>A000012</a></td>
    <td style = "text-align: left;">[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">RightSide</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A002426'>A002426</a></td>
    <td style = "text-align: left;">[1 1 3 7 19 51 141 393 1107 3139 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">PosHalf</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 3 11 39 139 493 1745 6163 21731 76521 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 3 11 39 139 493 1745 6163 21731 76521 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">NegHalf</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 -1 3 -1 11 9 57 111 387 989 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 -1 3 -1 11 9 57 111 387 989 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">PolyVal2</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 3 17 87 481 2663 14993 84983 485057 2782023 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 3 17 87 481 2663 14993 84983 485057 2782023 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">PolyVal3</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 4 34 253 2074 16999 142255 1199776 10203946 87281983 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 4 34 253 2074 16999 142255 1199776 10203946 87281983 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">BinConv</td>
    <td style = "text-align: left;"><a href='https://oeis.org/A082759'>A082759</a></td>
    <td style = "text-align: left;">[1 2 8 35 160 752 3599 17446 85376 420884 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">IBinConv</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 0 0 -3 0 0 15 0 0 -84 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 0 0 -3 0 0 15 0 0 -84 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">TransSqrs</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[0 1 14 90 492 2330 10206 42147 166872 639414 ]'>nomatch</a></td>
    <td style = "text-align: left;">[0 1 14 90 492 2330 10206 42147 166872 639414 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">TransNat0</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[0 1 8 36 148 560 2034 7161 24672 83592 ]'>nomatch</a></td>
    <td style = "text-align: left;">[0 1 8 36 148 560 2034 7161 24672 83592 ]</td>
  </tr>
  <tr>
    <td style = "text-align: left;">TransNat1</td>
    <td style = "text-align: left;"><a href='https://oeis.org/?q=[1 3 14 53 198 707 2469 8451 28506 95003 ]'>nomatch</a></td>
    <td style = "text-align: left;">[1 3 14 53 198 707 2469 8451 28506 95003 ]</td>
  </tr>
</table>