%I #31 Jun 18 2022 13:54:09
%S 1,1,1,3,4,5,8,10,12,17,21,24,31,37,42,52,60,67,80,91,101,117,131,144,
%T 164,182,198,222,244,264,293,319,343,377,408,437,476,512,546,591,633,
%U 672,723,771,816,874,928,979,1044,1105,1163,1235,1303,1368
%N 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.
%H T. D. Noe, <a href="/A028288/b028288.txt">Table of n, a(n) for n = 0..1000</a>
%H A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, <a href="http://arXiv.org/abs/quant-ph/9608006">Quantum error correction via codes over GF(4)</a>, IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
%H W. Duke, <a href="http://dx.doi.org/10.1155/S1073792893000121">On codes and Siegel modular forms</a>, Int. Math. Res. Notes 1993, No. 5, Theorem 2.
%H W. C. Huffman, <a href="http://dx.doi.org/10.1016/0012-365X(79)90119-5">The biweight enumerator of self-orthogonal binary codes</a>, Discr. Math. Vol. 26 1979, pp. 129-143.
%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%H E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (<a href="http://neilsloane.com/doc/self.txt">Abstract</a>, <a href="http://neilsloane.com/doc/self.pdf">pdf</a>, <a href="http://neilsloane.com/doc/self.ps">ps</a>).
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,1,-2,1,-2,2,0,1,-1).
%F G.f.: (1+x^4)/((1-x)*(1-x^3)^2*(1-x^5)).
%F a(n) ~ 1/135*n^3. - _Ralf Stephan_, Apr 29 2014
%p 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
%t 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 *)
%t CoefficientList[Series[(1+x^4)/((1-x)(1-x^3)^2(1-x^5)),{x,0,60}],x] (* _Harvey P. Dale_, Jul 10 2019 *)
%o (PARI) Vec((1+x^4)/((1-x)*(1-x^3)^2*(1-x^5)) + O('x^60)) \\ _G. C. Greubel_, Feb 01 2020
%o (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
%o (Sage)
%o def A028288_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1+x^4)/((1-x)*(1-x^3)^2*(1-x^5)) ).list()
%o A028288_list(60) # _G. C. Greubel_, Feb 01 2020
%Y Cf. A008621, A008718, A024186, A039946, A051263.
%K nonn,nice,easy
%O 0,4
%A _N. J. A. Sloane_