A090176 Expansion of (1+x^9)/((1-x^4)*(1-x^6)*(1-x^12)).

1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 3, 1, 1, 1, 3, 1, 3, 1, 3, 3, 3, 1, 6, 3, 3, 3, 6, 3, 6, 3, 6, 6, 6, 3, 10, 6, 6, 6, 10, 6, 10, 6, 10, 10, 10, 6, 15, 10, 10, 10, 15, 10, 15, 10, 15, 15, 15, 10, 21, 15, 15, 15, 21, 15, 21, 15, 21, 21, 21, 15, 28, 21, 21, 21, 28, 21, 28, 21, 28, 28, 28, 21, 36

Offset

0,13

Comments

Harmonic Molien series for real Clifford group C_2 of order 2304 is (1+x^18)/((1-x^8)(1-x^12)(1-x^24)).

Links

Table of n, a(n) for n=0..84.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,0,-1,0,0,0,0,1,0,0,-1,-1,0,0,1).

Formula

a(n) ~ 1/288*n^2. - Ralf Stephan, Apr 29 2014

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

a(n) = floor((n^2+24*n+288)/288 - (n+2)*(9*(n mod 2) + 4*(n mod 3))/144 + (((n+1)*(n+2)) mod 4)*n/48). - Hoang Xuan Thanh, Apr 26 2026

Prog

(PARI) Vec((1+x^9)/((1-x^4)*(1-x^6)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 10 2020

Crossrefs

Sequence in context: A309307 A325446 A337322 * A351544 A102396 A344852

Adjacent sequences: A090173 A090174 A090175 * A090177 A090178 A090179

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 05 2004

Status

approved