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%I #35 Sep 08 2022 08:44:36
%S 1,1,2,3,5,6,9,11,16,19,25,30,39,45,56,65,79,90,107,121,142,159,183,
%T 204,233,257,290,319,357,390,433,471,520,563,617,666,727,781,848,909,
%U 983,1050,1131,1205,1294,1375,1471,1560,1665,1761,1874,1979,2101,2214,2345,2467,2608,2739
%N Expansion of (1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
%C Molien series for 4-dimensional group of structure 2^{1+4}_{+}.S_3 and order 192, arising from complete weight enumerators of Euclidean self-dual linear codes over GF(4).
%H G. C. Greubel, <a href="/A008769/b008769.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 href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-2,0,0,1,1,-1).
%F a(n) = 1 + 5*n/72 - n^2/12 + n^3/72 + 1/2*floor(n/4) + 1/3*floor(n/3) + (1/4 + n/4)*floor(n/2) + 1/2*floor((1 + n)/4) + 1/3*floor((1 + n)/3). - _Vaclav Kotesovec_, Apr 29 2014
%F a(n) = round((n+1)*(2*n^2 + 4*n + 83 + 9*(-1)^n)/144). - _Tani Akinari_, May 13 2014
%p seq(coeff(series((1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)), x, n+1), x, n), n = 0 .. 60); # _G. C. Greubel_, Sep 10 2019
%t CoefficientList[Series[(1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 29 2014 *)
%o (PARI) a(n)=round((n+1)*(2*n^2+4*n+83+9*(-1)^n)/144) \\ _Tani Akinari_, May 13 2014
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // _G. C. Greubel_, Sep 10 2019
%o (Sage)
%o def A008769_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()
%o A008769_list(60) # _G. C. Greubel_, Sep 10 2019
%o (GAP) a:=[1,1,2,3,5,6,9,11,16,19];; for n in [11..60] do a[n]:=a[n-1] +a[n-2]-2*a[n-5]+a[n-8]+a[n-9]-a[n-10]; od; a; # _G. C. Greubel_, Sep 10 2019
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E Terms a(45) onward added by _G. C. Greubel_, Sep 10 2019