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A008769 Expansion of (1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)). 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..44.

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

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

CROSSREFS

Sequence in context: A230515 A030068 A239958 * A115270 A027588 A224956

Adjacent sequences:  A008766 A008767 A008768 * A008770 A008771 A008772

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)