OFFSET
1,7
COMMENTS
Row sums are 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
LINKS
Michael Gromov, Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits), Publications Math. de l'IHES, 53 (1981), p. 53-78; see p. 75
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.
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;
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]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 31 2008
STATUS
approved