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A008718
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G.f.: (1+x^9)/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)).
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8
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1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 9, 10, 11, 12, 15, 16, 19, 20, 23, 26, 29, 30, 36, 39, 42, 45, 51, 54, 60, 63, 69, 75, 81, 84, 94, 100, 106, 112, 122, 128, 138, 144, 154, 164, 174, 180, 195, 205, 215, 225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Molien series for genus-2 weight enumerators of binary self-dual codes is (1+x^18)/((1-x^2)*(1-x^8)*(1-x^12)*(1-x^24)). Exponents have been divided by 2 to get the sequence.
Or, Molien series for 4-dimensional representation of 2.{3,4,3}. This is the real 4-dimensional Clifford group of genus 2 and order 2304.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
F. J. MacWilliams, C. L. Mallows and N. J. A. Sloane, Generalizations of Gleason's theorem on weight enumerators of self-dual codes, IEEE Trans. Inform. Theory, 18 (1972), 794-805; see p. 802, col. 2, foot.
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
Index entries for Molien series
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MAPLE
| (x^9+1)/(1-x)/(1-x^4)/(-x^6+1)/(-x^12+1);
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MATHEMATICA
| CoefficientList[Series[(1+x^9)/((1-x)(1-x^4)(1-x^6) (1-x^12)), {x, 0, 60}], x] (* From Harvey P. Dale, Apr 1 2011 *)
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CROSSREFS
| Cf. A008621, A024186.
Sequence in context: A029071 A117144 A104408 * A030719 A126027 A111581
Adjacent sequences: A008715 A008716 A008717 * A008719 A008720 A008721
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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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