A091973 Poincaré series [or Poincare series] (or Molien series) for a certain three-dimensional group of order 1344.

1, 0, 1, 3, 3, 4, 7, 8, 9, 12, 14, 17, 20, 22, 26, 30, 32, 36, 42, 45, 49, 55, 59, 64, 70, 75, 81, 88, 93, 99, 107, 113, 120, 128, 135, 143, 151, 158, 167, 177, 184, 193, 204, 212, 221, 232, 242, 252, 263, 273, 284, 296, 306, 318, 331, 342, 354, 367, 379, 392, 406, 418, 432, 447

Offset

0,4

References

A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 259.

Links

Table of n, a(n) for n=0..63.

Index entries for linear recurrences with constant coefficients, signature (1,-1,2,-1,1,-1,1,-1,1,-2,1,-1,1).

Formula

G.f.: (1 + x^2 + 3*x^3 + 2*x^4 + 4*x^5 + 5*x^6 + 4*x^7 + 5*x^8 + 4*x^9 + 2*x^10 + 3*x^11 + x^12 + x^14 ) / ( (1-x^4)*(1-x^6)*(1-x^7)).

G.f.: ( -1-2*x^2-x^5-x^10+x-2*x^4-2*x^6-2*x^8+x^9 ) / ( (1+x+x^2) *(x^6+x^5+x^4+x^3+x^2+x+1) *(1+x^2) *(x-1)^3 ). - R. J. Mathar, Dec 18 2014

Mathematica

LinearRecurrence[{1, -1, 2, -1, 1, -1, 1, -1, 1, -2, 1, -1, 1}, {1, 0, 1, 3, 3, 4, 7, 8, 9, 12, 14, 17, 20}, 64]
(* Ray Chandler, Jul 15 2015 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, -1, 1, -2, 1, -1, 1, -1, 1, -1, 2, -1, 1]^n*[1; 0; 1; 3; 3; 4; 7; 8; 9; 12; 14; 17; 20])[1, 1] \\ Charles R Greathouse IV, May 01 2020

Crossrefs

Sequence in context: A349252 A152651 A343396 * A328798 A327726 A050066

Adjacent sequences: A091970 A091971 A091972 * A091974 A091975 A091976

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 18 2004

Status

approved