A008772 - OEIS

%I #23 Feb 29 2024 15:45:09

%S 1,1,2,3,5,6,9,11,15,18,23,28,35,41,50,59,70,81,95,109,126,143,163,

%T 184,208,232,260,289,321,354,391,429,471,514,561,610,663,717,776,837,

%U 902,969,1041,1115,1194,1275,1361,1450,1544,1640,1742,1847,1957,2070,2189,2311,2439,2570,2707

%N Expansion of (1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

%H Vincenzo Librandi, <a href="/A008772/b008772.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1,-1,1,-1,2,-1).

%F G.f.: (1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

%p seq(coeff(series((1+x^11)/((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^11)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4), {x,0,60}], x] (* _Wesley Ivan Hurt_, Apr 08 2017 *)

%t Join[{1, 1}, LinearRecurrence[{2,-1,1,-1,-1,1,-1,2,-1}, {2,3,5,6,9,11,15, 18,23}, 60]] (* _Vincenzo Librandi_, Apr 09 2017 *)

%o (PARI) Vec((1+x^11)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4) + O(x^60)) \\ _Michel Marcus_, Apr 08 2017

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // _G. C. Greubel_, Sep 10 2019

%o (Sage)

%o def A008772_list(prec):

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

%o     return P((1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()

%o A008772_list(60) # _G. C. Greubel_, Sep 10 2019

%o (GAP) a:=[2,3,5,6,9,11,15,18,23];; for n in [10..60] do a[n]:=2*a[n-1]-a[n-2]+a[n-3]-a[n-4]-a[n-5]+a[n-6]-a[n-7]+2*a[n-8]-a[n-9]; od; Concatenation([1,1], a); # _G. C. Greubel_, Sep 10 2019

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Sep 10 2019