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A028288
Molien series for complex 4-dimensional Clifford group of order 92160 and genus 2. Also Molien series of ring of biweight enumerators of Type II self-dual binary codes.
4
1, 1, 1, 3, 4, 5, 8, 10, 12, 17, 21, 24, 31, 37, 42, 52, 60, 67, 80, 91, 101, 117, 131, 144, 164, 182, 198, 222, 244, 264, 293, 319, 343, 377, 408, 437, 476, 512, 546, 591, 633, 672, 723, 771, 816, 874, 928, 979, 1044, 1105, 1163, 1235, 1303, 1368
OFFSET
0,4
LINKS
A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4), IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
W. Duke, On codes and Siegel modular forms, Int. Math. Res. Notes 1993, No. 5, Theorem 2.
W. C. Huffman, The biweight enumerator of self-orthogonal binary codes, Discr. Math. Vol. 26 1979, pp. 129-143.
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
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 (1,0,2,-2,1,-2,1,-2,2,0,1,-1).
FORMULA
G.f.: (1+x^4)/((1-x)*(1-x^3)^2*(1-x^5)).
a(n) ~ 1/135*n^3. - Ralf Stephan, Apr 29 2014
MAPLE
seq(coeff(series((1+x^4)/((1-x)*(1-x^3)^2*(1-x^5)), x, n+1), x, n), n = 0..60); # G. C. Greubel, Feb 01 2020
MATHEMATICA
LinearRecurrence[{1, 0, 2, -2, 1, -2, 1, -2, 2, 0, 1, -1}, {1, 1, 1, 3, 4, 5, 8, 10, 12, 17, 21, 24}, 60] (* Jean-François Alcover, Jan 27 2015 *)
CoefficientList[Series[(1+x^4)/((1-x)(1-x^3)^2(1-x^5)), {x, 0, 60}], x] (* Harvey P. Dale, Jul 10 2019 *)
PROG
(PARI) Vec((1+x^4)/((1-x)*(1-x^3)^2*(1-x^5)) + O('x^60)) \\ G. C. Greubel, Feb 01 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^4)/((1-x)*(1-x^3)^2*(1-x^5)) )); // G. C. Greubel, Feb 01 2020
(Sage)
def A028288_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x^4)/((1-x)*(1-x^3)^2*(1-x^5)) ).list()
A028288_list(60) # G. C. Greubel, Feb 01 2020
CROSSREFS
KEYWORD
nonn,nice,easy
STATUS
approved