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.

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

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

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 Molien series

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

Cf. A008621, A008718, A024186, A039946, A051263.

Sequence in context: A213513 A344168 A239142 * A118250 A278998 A211533

Adjacent sequences: A028285 A028286 A028287 * A028289 A028290 A028291

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved