A004657 - OEIS

%I #22 Sep 08 2022 08:44:33

%S 1,1,3,4,9,11,19,24,37,45,63,76,101,119,151,176,217,249,299,340,401,

%T 451,523,584,669,741,839,924,1037,1135,1263,1376,1521,1649,1811,1956,

%U 2137,2299,2499,2680,2901,3101

%N Expansion of g.f.: (1+x^3)*(1+x^4)/((1-x)*(1-x^2)^2*(1-x^4)).

%D M. Klemm, Selbstduale Codes ueber dem Ring der ganzen Zahlen modulo 4, Arch. Math. (Basel), 53 (1989), 201-207.

%H G. C. Greubel, <a href="/A004657/b004657.txt">Table of n, a(n) for n = 0..1000</a>

%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 A. R. Calderbank and N. J. A. Sloane, Double circulant codes over Z_4, J. Algeb. Combin., 6 (1997) 119-131 (<a href="http://neilsloane.com/doc/mckay.txt">Abstract</a>, <a href="http://neilsloane.com/doc/mckay.pdf">pdf</a>, <a href="http://neilsloane.com/doc/mckay.ps">ps</a>).

%H <a href="/index/Mo#Molien">Index entries for Molien series</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2,-2,0,2,-1).

%F G.f.: (x^2-x+1)*(1+x^4) / ( (x^2+1)*(1+x)^2*(x-1)^4 ). - _R. J. Mathar_, Dec 18 2014

%t CoefficientList[Series[(x^2 - x + 1)*(1 + x^4)/((x^2 + 1)*(1 + x)^2*(x - 1)^4), {x, 0, 50}], x] (* _G. C. Greubel_, Sep 10 2018 *)

%o (PARI) x='x+O('x^50); Vec((x^2-x+1)*(1+x^4)/((x^2+1)*(1+x)^2*(x-1)^4)) \\ _G. C. Greubel_, Sep 10 2018

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((x^2-x+1)*(1+x^4)/((x^2+1)*(1+x)^2*(x-1)^4))); // _G. C. Greubel_, Sep 10 2018

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E Definition corrected by _N. J. A. Sloane_, Apr 08 2004