|
%I #21 Sep 08 2022 08:44:36
%S 1,1,2,3,4,5,7,8,11,13,16,19,23,26,31,35,40,45,51,56,63,69,76,83,91,
%T 98,107,115,124,133,143,152,163,173,184,195,207,218,231,243,256,269,
%U 283,296,311,325,340,355
%N Expansion of (1+x^8)/((1-x)*(1-x^2)*(1-x^3)).
%H Vincenzo Librandi, <a href="/A008751/b008751.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
%F From _Henry Bottomley_, Sep 05 2000: (Start)
%F a(n) = floor((n^2 - 2*n + 18)/6) for n>2.
%F a(n) = a(n-2) + a(n-3) - a(n-5) + 2.
%F a(n) = A001399(n) + A001399(n-8).
%F a(n) = A008747(n-2) + 2 for n>2. (End)
%t CoefficientList[Series[(1+x^8)/((1-x)(1-x^2)(1-x^3)),{x,0,50}],x] (* _Vincenzo Librandi_, Feb 25 2012 *)
%t Join[{1,1,2}, Floor[((Range[3, 50] -1)^2 +17)/6]] (* _G. C. Greubel_, Aug 04 2019 *)
%o (PARI) my(x='x+O('x^50)); Vec((1+x^8)/((1-x)*(1-x^2)*(1-x^3))) \\ _G. C. Greubel_, Aug 04 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^8)/((1-x)*(1-x^2)*(1-x^3)) )); // _G. C. Greubel_, Aug 04 2019
%o (Sage) ((1+x^8)/((1-x)*(1-x^2)*(1-x^3))).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 04 2019
%o (GAP) Concatenation([1,1,2], List([3..50], n-> Int(((n-1)^2 +17)/6))); # _G. C. Greubel_, Aug 04 2019
%Y Cf. A001399, A008747.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
|
