%I #13 Sep 08 2022 08:44:36
%S 1,0,2,0,3,2,4,4,7,6,10,8,13,12,16,16,21,20,26,24,31,30,36,36,43,42,
%T 50,48,57,56,64,64,73,72,82,80,91,90,100,100,111,110,122,120,133,132,
%U 144,144,157,156,170,168,183,182,196,196,211,210,226,224,241,240
%N Expansion of (1+2*x^5+x^8)/((1-x^2)^2*(1-x^8)).
%H Harvey P. Dale, <a href="/A008819/b008819.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,0,0,1,-1,-1,1).
%F a(0)=1, a(1)=0, a(2)=2, a(3)=0, a(4)=3, a(5)=2, a(6)=4, a(7)=4, a(8)=7, a(9)=6, a(10)=10, a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-8) - a(n-9) - a(n-10) + a(n-11). - _Harvey P. Dale_, Oct 28 2015
%p seq(coeff(series((1+2*x^5+x^8)/((1-x^2)^2*(1-x^8)), x, n+1), x, n), n = 0..60); # _G. C. Greubel_, Sep 12 2019
%t CoefficientList[Series[(1+2x^5+x^8)/(1-x^2)^2/(1-x^8), {x,0,60}], x] (* or *) LinearRecurrence[{1,1,-1,0,0,0,0,1,-1,-1,1}, {1,0,2,0,3,2,4,4,7, 6,10}, 60] (* _Harvey P. Dale_, Oct 28 2015 *)
%o (PARI) my(x='x+O('x^60)); Vec((1+2*x^5+x^8)/((1-x^2)^2*(1-x^8))) \\ _G. C. Greubel_, Sep 12 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+2*x^5+x^8)/((1-x^2)^2*(1-x^8)) )); // _G. C. Greubel_, Sep 12 2019
%o (Sage)
%o def A008819_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1+2*x^5+x^8)/((1-x^2)^2*(1-x^8))).list()
%o A008819_list(60) # _G. C. Greubel_, Sep 12 2019
%o (GAP) a:=[1,0,2,0,3,2,4,4,7,6,10];; for n in [12..60] do a[n]:=a[n-1] +a[n-2]-a[n-3]+a[n-8]-a[n-9]-a[n-10]+a[n-11]; od; a; # _G. C. Greubel_, Sep 12 2019
%Y Cf. Expansions of the form (1 +2*x^(2*m+1) +x^(4*m))/((1-x^2)^2*(1-x^(4*m))): A008818 (m=1), this sequence (m=2), A008820 (m=3), A008821 (m=4).
%K nonn
%O 0,3
%A _N. J. A. Sloane_