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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
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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; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Row sums are 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
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LINKS
| 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;
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FORMULA
| 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
| 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
| 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
| Sequence in context: A151706 A055372 A198285 * A139548 A193378 A108445
Adjacent sequences: A136617 A136618 A136619 * A136621 A136622 A136623
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KEYWORD
| uned,tabl,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 31 2008
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