A107351 Expansion of (1+x^3)/((1-x)^3*(1-x^2)^3*(1-x^3)).

1, 3, 9, 21, 45, 87, 159, 273, 450, 712, 1092, 1626, 2364, 3360, 4686, 6420, 8661, 11517, 15121, 19617, 25179, 31995, 40287, 50295, 62298, 76596, 93534, 113482, 136860, 164118, 195762, 232332, 274431, 322701, 377853, 440643, 511903, 592515, 683445, 785715

Offset: 0

Author

N. J. A. Sloane, May 23 2005

Keywords

• nonn
• easy

References

• Y. Teranishi, Linear Diophantine equations and invariant theory of matrices, in Commutative algebra and combinatorics (Kyoto, 1985), pp. 259-275, Adv. Stud. Pure Math., 11, North-Holland, Amsterdam, 1987.

Links

• Index entries for Molien series
• Index entries for linear recurrences with constant coefficients, signature (4,-4,-3,6,0,0,-6,3,4,-4,1).

Formula

G.f.: ( -1+x-x^2 ) / ( (1+x+x^2)*(1+x)^2*(x-1)^7 ). - R. J. Mathar, Dec 18 2014

81*a(n) = 2*A099837(n+3) +(134946*n +22680*n^3 +77688*n^2 +3690*n^4 +324*n^5 +12*n^6 +87625)/1280 +(-1)^n*243 *(9+2*n)/256 . - R. J. Mathar, Dec 17 2017