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 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
AUTHOR
STATUS
approved