A097992 G.f.: 1/((1-x)*(1-x^6)) = 1/ ( (1+x)*(x^2-x+1)*(1+x+x^2)*(x-1)^2 ).

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15

Offset: 0

Author

N. J. A. Sloane, Sep 07 2004

Keywords

• nonn

Links

• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
• Index entries for Molien series
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Crossrefs

Apart from initial terms, same as A054895.

Programs

Mathematica

CoefficientList[Series[1/((1-x)(1-x^6)),{x,0,90}],x] (* or *) LinearRecurrence[{1,0,0,0,0,1,-1},{1,1,1,1,1,1,2},90] (* Harvey P. Dale, Oct 29 2023 *)

Formula

Molien series is 1/((1-x^2)*(1-x^12)).

a(n)=1+floor(n/6)

a(n)=1+(6*n-15+3*(-1)^n+12*sin[(2*n+1)*Pi/6]+4*sqrt(3)*sin[(2*n+1)*Pi/3])/36