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A097869
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Expansion of g.f.: (1+x^4+x^5+x^9)/((1-x)*(1-x^2)*(1-x^4)^2).
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3
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1, 1, 2, 2, 6, 7, 11, 12, 21, 25, 34, 38, 54, 63, 79, 88, 113, 129, 154, 170, 206, 231, 267, 292, 341, 377, 426, 462, 526, 575, 639, 688, 769, 833, 914, 978, 1078, 1159, 1259, 1340, 1461, 1561, 1682, 1782, 1926, 2047, 2191, 2312, 2481, 2625, 2794, 2938, 3134, 3303
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OFFSET
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0,3
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COMMENTS
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Molien series for group of order 128 acting on joint weight enumerators of a pair of binary self-dual codes is (1+x^8+x^10+x^18)/((1-x^2)*(1-x^4)*(1-x^8)^2).
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,-1,0,2,-4,2,0,-1,2,-1).
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FORMULA
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G.f.: (1+x^4)*(1-x+x^2-x^3+x^4)/( (1+x)^2*(1+x^2)^2*(1-x)^4 ). - R. J. Mathar, Dec 18 2014
a(2*n) = (1/48)*(30 + 18*(-1)^n + 64*n + 12*n^2 + 8*n^3),
a(2*n+1) = (1/48)*(36 + 12*(-1)^n + 16*n + 8*n^2)*(1 + n). (End)
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MAPLE
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m:=55; S:=series((1+x^4)*(1+x^5)/((1-x)*(1-x^2)*(1-x^4)^2), x, m+1): seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Feb 05 2020
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MATHEMATICA
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CoefficientList[Series[(1+x^4)*(1+x^5)/((1-x)*(1-x^2)*(1-x^4)^2), {x, 0, 55}], x] (* G. C. Greubel, Feb 05 2020 *)
LinearRecurrence[{2, -1, 0, 2, -4, 2, 0, -1, 2, -1}, {1, 1, 2, 2, 6, 7, 11, 12, 21, 25}, 60] (* Harvey P. Dale, Jun 19 2021 *)
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PROG
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(PARI) Vec( (1+x^4)*(1+x^5)/((1-x)*(1-x^2)*(1-x^4)^2) +O('x^55) ) \\ G. C. Greubel, Feb 05 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 55); Coefficients(R!( (1+x^4)*(1+x^5)/((1-x)*(1-x^2)*(1-x^4)^2) )); // G. C. Greubel, Feb 05 2020
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x^4)*(1+x^5)/((1-x)*(1-x^2)*(1-x^4)^2) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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