A008769 Expansion of (1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

1, 1, 2, 3, 5, 6, 9, 11, 16, 19, 25, 30, 39, 45, 56, 65, 79, 90, 107, 121, 142, 159, 183, 204, 233, 257, 290, 319, 357, 390, 433, 471, 520, 563, 617, 666, 727, 781, 848, 909, 983, 1050, 1131, 1205, 1294, 1375, 1471, 1560, 1665, 1761, 1874, 1979, 2101, 2214, 2345, 2467, 2608, 2739

Offset

0,3

Comments

Molien series for 4-dimensional group of structure 2^{1+4}_{+}.S_3 and order 192, arising from complete weight enumerators of Euclidean self-dual linear codes over GF(4).

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.

Index entries for Molien series

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

Formula

a(n) = 1 + 5*n/72 - n^2/12 + n^3/72 + 1/2*floor(n/4) + 1/3*floor(n/3) + (1/4 + n/4)*floor(n/2) + 1/2*floor((1 + n)/4) + 1/3*floor((1 + n)/3). - Vaclav Kotesovec, Apr 29 2014

a(n) = round((n+1)*(2*n^2 + 4*n + 83 + 9*(-1)^n)/144). - Tani Akinari, May 13 2014

Maple

seq(coeff(series((1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)), x, n+1), x, n), n = 0 .. 60); # G. C. Greubel, Sep 10 2019

Mathematica

CoefficientList[Series[(1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 29 2014 *)

Prog

(PARI) a(n)=round((n+1)*(2*n^2+4*n+83+9*(-1)^n)/144)  \\ Tani Akinari, May 13 2014
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // G. C. Greubel, Sep 10 2019
(Sage)
def A008769_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()
A008769_list(60) # G. C. Greubel, Sep 10 2019
(GAP) a:=[1, 1, 2, 3, 5, 6, 9, 11, 16, 19];; for n in [11..60] do a[n]:=a[n-1] +a[n-2]-2*a[n-5]+a[n-8]+a[n-9]-a[n-10]; od; a; # G. C. Greubel, Sep 10 2019

Crossrefs

Sequence in context: A230515 A030068 A239958 * A115270 A339277 A027588

Adjacent sequences: A008766 A008767 A008768 * A008770 A008771 A008772

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Terms a(45) onward added by G. C. Greubel, Sep 10 2019

Status

approved