A008773 - OEIS

%I #17 Sep 08 2022 08:44:36

%S 1,1,2,3,5,6,9,11,15,18,23,27,35,40,49,57,69,78,93,105,123,138,159,

%T 177,203,224,253,279,313,342,381,415,459,498,547,591,647,696,757,813,

%U 881,942,1017,1085,1167,1242,1331,1413,1511,1600,1705,1803,1917,2022,2145

%N Expansion of (1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

%H G. C. Greubel, <a href="/A008773/b008773.txt">Table of n, a(n) for n = 0..1000</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).

%p seq(coeff(series((1+x^12)/((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^12)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4), {x,0,60}], x] (* _Stefan Steinerberger_, Apr 08 2006 *)

%t Join[{1,1,2}, LinearRecurrence[{1,1,0,0,-2,0,0,1,1,-1}, {3,5,6,9,11,15, 18,23,27,35}, 60]] (* _G. C. Greubel_, Sep 10 2019 *)

%o (PARI) my(x='x+O('x^60)); Vec((1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))) \\ _G. C. Greubel_, Sep 10 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // _G. C. Greubel_, Sep 10 2019

%o (Sage)

%o def A008773_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P((1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()

%o A008773_list(60) # _G. C. Greubel_, Sep 10 2019

%o (GAP) a:=[3,5,6,9,11,15,18,23,27,35];; 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; Concatenation([1,1,2], a); # _G. C. Greubel_, Sep 10 2019

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Stefan Steinerberger_, Apr 08 2006