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A008647 G.f.: (1+x^9)/((1-x^4)*(1-x^6)) = ( 1+x^6-x^3 ) / ( (1+x)*(1+x+x^2)*(x^2+1)*(x-1)^2 ). 2
1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 4, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4, 3, 5, 4, 4, 4, 5, 4, 5, 4, 5, 5, 5, 4, 6, 5, 5, 5, 6, 5, 6, 5, 6, 6, 6, 5, 7, 6, 6, 6, 7, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

Molien series of binary octahedral group of order 48. Also Molien series for W_1 - W_3 of shadow of singly-even binary self-dual code.

REFERENCES

T. A. Springer, Invariant Theory, Lecture Notes in Math., Vol. 585, Springer, p. 97.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Eiichi Bannai, Etsuko Bannai, Michio Ozeki and Yasuo Teranishi, On the ring of simultaneous invariants for the Gleason-MacWilliams group, European J. Combin. 20 (1999), 619-627.

J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, 36 (1990), 1319-1334.

E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).

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

Index entries for Molien series

FORMULA

G.f.: (1+x^18)/((1-x^8)*(1-x^12). Also (1+x^6+x^9+x^15)/((1-x^4)*(1-x^12)).

It appears that the first differences have period 12. Hence in blocks of 12, the sequence is {1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0}+k for k=0,1,2,... - T. D. Noe, May 23 2008

a(n) = A057077(n)/4+A057078(n)/3+1/24+n/12+3/8*(-1)^n. - R. J. Mathar, Jun 28 2009

a(n) = a(n-3)+ a(n-4)-a(n-7), a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=0, a(6)=1. - Harvey P. Dale, Oct 10 2011

a(n) = floor((9*(-1)^n+2*(n+7)+6*(-1)^floor(n/2))/24). - Tani Akinari, Jun 17 2013

MAPLE

g:= proc(n) local m, r; m:= iquo(n, 12, 'r'); irem(r+1, 2) *(m+1) -`if`(r=2, 1, 0) end: a:= n-> g(n) +`if`(n>8, g(n-9), 0); seq(a(n), n=0..1000); # Alois P. Heinz, Oct 06 2008

MATHEMATICA

CoefficientList[Series[(1+x^9)/((1-x^4)*(1-x^6)), {x, 0, 80}], x] (* or *) LinearRecurrence[{0, 0, 1, 1, 0, 0, -1}, {1, 0, 0, 0, 1, 0, 1}, 80] (* Harvey P. Dale, Oct 10 2011 *)

PROG

(PARI) a(n)=(9*(-1)^n+2*(n+7)+6*(-1)^(n\2))\24 \\ Charles R Greathouse IV, Feb 10 2017

CROSSREFS

Sequence in context: A050320 A121382 A051265 * A036475 A187279 A076820

Adjacent sequences:  A008644 A008645 A008646 * A008648 A008649 A008650

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 24 06:43 EDT 2017. Contains 293836 sequences.