A228707 G.f.: (1-3*x+5*x^2-5*x^3+5*x^4-5*x^5+5*x^6-3*x^7+x^8)/((1-x)^4*(1+x^4)*(1+x^2)^2).

1, 1, 1, 3, 6, 8, 10, 16, 24, 29, 35, 47, 61, 72, 84, 104, 127, 145, 165, 195, 228, 256, 286, 328, 374, 413, 455, 511, 571, 624, 680, 752, 829, 897, 969, 1059, 1154, 1240, 1330, 1440, 1556, 1661, 1771, 1903, 2041, 2168, 2300, 2456, 2619, 2769

Offset: 0

Author

N. J. A. Sloane, Sep 06 2013

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• E. Kirkman, J. Kuzmanovich and J. J. Zhang, Invariants of (-1)-Skew Polynomial Rings under Permutation Representations, arXiv preprint arXiv:1305.3973, 2013

Crossrefs

Cf. A032279, A228706.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x+5*x^2-5*x^3+5*x^4-5*x^5+5*x^6-3*x^7+x^8)/((1-x)^4*(1+x^4)*(1+x^2)^2))); // Vincenzo Librandi, Sep 07 2013

Mathematica

CoefficientList[Series[(1 - 3 x + 5 x^2 - 5 x^3 + 5 x^4 - 5 x^5 + 5 x^6 - 3 x^7 + x^8) / ((1 - x)^4 (1 + x^4) (1 + x^2)^2), {x, 0, 50}],x] (* Vincenzo Librandi, Sep 07 2013 *)

Formula

G.f.: (1-x+x^2)*(1-2 *x+2*x^2-x^3+2*x^4-2*x^5+x^6)/((1+x^2)^2*(1-x)^4*(1+x^4)).