A004657 Expansion of g.f.: (1+x^3)*(1+x^4)/((1-x)*(1-x^2)^2*(1-x^4)).

1, 1, 3, 4, 9, 11, 19, 24, 37, 45, 63, 76, 101, 119, 151, 176, 217, 249, 299, 340, 401, 451, 523, 584, 669, 741, 839, 924, 1037, 1135, 1263, 1376, 1521, 1649, 1811, 1956, 2137, 2299, 2499, 2680, 2901, 3101

Offset

0,3

References

M. Klemm, Selbstduale Codes ueber dem Ring der ganzen Zahlen modulo 4, Arch. Math. (Basel), 53 (1989), 201-207.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

A. R. Calderbank and N. J. A. Sloane, Double circulant codes over Z_4, J. Algeb. Combin., 6 (1997) 119-131 (Abstract, pdf, ps).

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,2,-2,0,2,-1).

Formula

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

Mathematica

CoefficientList[Series[(x^2 - x + 1)*(1 + x^4)/((x^2 + 1)*(1 + x)^2*(x - 1)^4), {x, 0, 50}], x] (* G. C. Greubel, Sep 10 2018 *)

Prog

(PARI) x='x+O('x^50); Vec((x^2-x+1)*(1+x^4)/((x^2+1)*(1+x)^2*(x-1)^4)) \\ G. C. Greubel, Sep 10 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((x^2-x+1)*(1+x^4)/((x^2+1)*(1+x)^2*(x-1)^4))); // G. C. Greubel, Sep 10 2018

Crossrefs

Sequence in context: A176744 A023420 A376654 * A054075 A366753 A062798

Adjacent sequences: A004654 A004655 A004656 * A004658 A004659 A004660

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Definition corrected by N. J. A. Sloane, Apr 08 2004

Status

approved