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Search: id:A137347
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| A137347 |
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Triangular sequence from coefficients of a polynomial recursion: p(x, n] = x*p(x, n - 1) - 2*x^2*p(x, n - 2) + x^3*p(x, n - 3). |
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+0
1
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| 1, -1, 1, 0, -1, -1, 0, 0, 1, -2, 0, 0, 0, 2, 1, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 7, -3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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1,10
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COMMENT
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Row sums are:
{1, 0, -2, -1, 3, 3, -4, -7, 4, 14, -1, -25, -9, 40, 33, -56}
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FORMULA
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p(x, n] = x*p(x, n - 1) - 2*x^2*p(x, n - 2) + x^3*p(x, n - 3).
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EXAMPLE
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{1},
{-1, 1},
{0, -1, -1},
{0, 0, 1, -2},
{0, 0, 0, 2, 1},
{0, 0, 0, 0, -1, 4},
{0, 0, 0, 0, 0, -4},
{0, 0, 0, 0, 0, 0, 0, -7},
{0, 0, 0, 0, 0, 0, 0, 7, -3},
{0, 0, 0, 0, 0, 0, 0, 0, 3, 11},
{0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10},
{0, 0, 0, 0, 0,0, 0, 0, 0, 0, -10, -15},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,15, -24},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 16},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 49},
{0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, -49, -7}
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MATHEMATICA
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Clear[p, x, a0, b0] p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = x - 1; p[x_, n_] := p[x, n] = x*p[x, n - 1] - 2*x^2*p[x, n - 2] + x^3*p[x, n - 3]; g = Table[ExpandAll[p[x, n]], {n, 0, 15}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 15}]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A137344 A137345 A137346 this_sequence A137348 A137349 A137350
Sequence in context: A079169 A097106 A088886 this_sequence A024941 A100699 A108921
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 08 2008
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