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

0,7

Links

Table of n, a(n) for n=0..88.

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).

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

G.f.: 1/(1 - x - x^6 + x^7). - Charles R Greathouse IV, May 20 2026

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 *)

Prog

(PARI) a(n)=n\6+[1, 1, 1, 1, 1, 1][n%6+1] \\ Charles R Greathouse IV, May 20 2026

Crossrefs

Apart from initial terms, same as A054895.

Sequence in context: A340764 A152467 A242602 * A195177 A147583 A054895

Adjacent sequences: A097989 A097990 A097991 * A097993 A097994 A097995

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 07 2004

Status

approved