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A008647
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G.f.: (1+x^9)/((1-x^4)*(1-x^6)).
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2
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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; internal format)
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OFFSET
| 0,13
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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.
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REFERENCES
| Bannai, Eiichi; Bannai, Etsuko; Ozeki, Michio; and Teranishi, Yasuo, 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.
T. A. Springer, Invariant Theory, Lecture Notes in Math., Vol. 585, Springer, p. 97.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
Index entries for sequences related to linear recurrences with constant coefficients
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 Molien series
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FORMULA
| (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. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 28 2009]
a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=0, a(6)=1, a(n)=a(n-3)+ a(n-4)-a(n-7) [From Harvey P. Dale, Oct 10 2011]
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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); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 06 2008]
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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] (* From Harvey P. Dale, Oct 10 2011 *)
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CROSSREFS
| Sequence in context: A050320 A121382 A051265 * A036475 A187279 A076820
Adjacent sequences: A008644 A008645 A008646 * A008648 A008649 A008650
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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