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Search: id:A136620
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| A136620 |
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Triangle of coefficients from polynomial recursion suggested by an equation in a paper by M. Gromov in the appendix by Jacques Tits on page 75: P(x,n)=(1-x)*P(x,n-1)-binomial[x-1,2]*P(x,n-2). |
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+0
1
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| 1, 1, -1, 0, -1, 1, -2, 4, -2, -4, 14, -17, 8, -1, 0, 4, -13, 15, -7, 1, 8, -32, 46, -25, -1, 5, -1, 8, -48, 116, -144, 96, -32, 4, 0, -24, 132, -300, 361, -244, 90, -16, 1, -16, 96, -228, 252, -79, -109, 134, -62, 13, -1, -32, 272, -984, 1980, -2416, 1811, -787, 154, 10, -9, 1
(list; table; graph; listen)
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OFFSET
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1,7
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COMMENT
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Row sums are:
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
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REFERENCES
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Gromov, Michael, Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits). Publications Math. de l'IHES, 53 (1981), p. 53-78; http://www.numdam.org/numdam-bin/fitem?id=PMIHES_1981__53__53_0.
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FORMULA
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P[x, -1] = 0; P[x, 0] = 1; P[x, 1] = 1 - x; P(x,n)=(1-x)*P(x,n-1)-binomial[x-1,2]*P(x,n-2) Output as 2^Floor[n/2]*P(x,n) to get Integers.
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EXAMPLE
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{1},
{1, -1},
{0, -1, 1},
{-2, 4, -2},
{-4, 14, -17,8, -1},
{0, 4, -13, 15, -7, 1},
{8, -32, 46, -25, -1, 5, -1},
{8, -48, 116, -144, 96, -32, 4},
{0, -24, 132, -300, 361, -244,90, -16, 1},
{-16, 96, -228, 252, -79, -109, 134, -62, 13, -1},
{-32, 272, -984, 1980, -2416, 1811, -787, 154, 10, -9, 1}
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MATHEMATICA
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P[x, -1] = 0; P[x, 0] = 1; P[x, 1] = 1 - x; P[x_, n_] := P[x, n] = (1 - x)*P[x, n - 1] - Binomial[x - 1, 2]*P[x, n - 2]; Table[ExpandAll[2^Floor[n/2]*P[x, n]], {n, 0, 10}]; a = Table[CoefficientList[2^Floor[n/2]*P[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A136617 A136618 A136619 this_sequence A136621 A136622 A136623
Sequence in context: A143107 A051638 A055372 this_sequence A139548 A108445 A019294
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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), Mar 31 2008
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