A008756 - OEIS

%I #15 Sep 08 2022 08:44:36

%S 1,1,2,3,4,5,7,8,10,12,14,16,19,22,25,29,33,37,42,47,52,58,64,70,77,

%T 84,91,99,107,115,124,133,142,152,162,172,183,194,205,217,229,241,254,

%U 267,280,294,308,322

%N Expansion of (1+x^13)/((1-x)*(1-x^2)*(1-x^3)).

%H G. C. Greubel, <a href="/A008756/b008756.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 1, -2, 1).

%F a(n) = (92 - 15*(n+1) + 3*A000217(n+1) + A061347(n+1))/9 for n > 7. - _R. J. Mathar_, Feb 19 2008

%t CoefficientList[Series[(1+x^13)/((1-x)*(1-x^2)*(1-x^3)), {x,0,60}], x] (* _G. C. Greubel_, Aug 04 2019 *)

%o (PARI) my(x='x+O('x^60)); Vec((1+x^13)/((1-x)*(1-x^2)*(1-x^3))) \\ _G. C. Greubel_, Aug 04 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^13)/((1-x)*(1-x^2)*(1-x^3)) )); // _G. C. Greubel_, Aug 04 2019

%o (Sage) ((1+x^13)/((1-x)*(1-x^2)*(1-x^3))).series(x, 60).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 04 2019

%o (GAP) a:=[8,10,12,14,16,19];; for n in [7..60] do a[n]:=2*a[n-1]-a[n-2] +a[n-3]-2*a[n-4]+a[n-5]; od; Concatenation([1,1,2,3,4,5,7], a); # _G. C. Greubel_, Aug 04 2019

%Y Cf. A000217, A061347.

%K nonn

%O 0,3

%A _N. J. A. Sloane_