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A136450
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Matrix based on counter variant Hankel matrix: ( smaller at central anti-diagonal) h(i,j)=If[i + j - 1 > n, 0, n + 1 - (i + j - 1) Characteristic polynomials as a triangle of coefficients.
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0
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1, 1, -1, -1, -2, 1, -1, 2, 4, -1, 1, 2, -7, -6, 1, 1, -2, -10, 12, 9, -1, -1, -2, 13, 18, -26, -12, 1, -1, 2, 16, -24, -52, 40, 16, -1, 1, 2, -19, -30, 87, 86, -70, -20, 1, 1, -2, -22, 36, 131, -150, -190, 100, 25, -1, -1, -2, 25, 42, -184, -232, 403, 294, -155, -30, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| These polynomials grow slower than their Hankel counterparts.
Row sums are:
{1, 0, -2, 4, -9, 9, -9, -4, 38, -72, 161}
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FORMULA
| h(i,j)=If[i + j - 1 > n, 0, n + 1 - (i + j - 1): i,j<=n
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EXAMPLE
| {1},
{1, -1},
{-1, -2, 1},
{-1, 2, 4, -1},
{1, 2, -7, -6, 1},
{1, -2, -10,12, 9, -1},
{-1, -2, 13, 18, -26, -12, 1},
{-1, 2, 16, -24, -52, 40, 16, -1},
{1, 2, -19, -30, 87, 86, -70, -20, 1},
{1, -2, -22, 36,131, -150, -190, 100, 25, -1},
{-1, -2, 25, 42, -184, -232,403, 294, -155, -30, 1}
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MATHEMATICA
| H[n_] := Table[Table[If[i + j - 1 > n, 0, n + 1 - (i + j - 1)], {i, 1, n}], {j, 1, n}]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[H[n], x], x], {n, 1, 10}]]; Flatten[a]
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CROSSREFS
| Sequence in context: A181802 A110971 A136788 * A131054 A166288 A056648
Adjacent sequences: A136447 A136448 A136449 * A136451 A136452 A136453
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KEYWORD
| uned,tabl,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 19 2008
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