login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 4 06:02 EDT 2021. Contains 346442 sequences. (Running on oeis4.)