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Expansion of (1+x^17)/((1-x)*(1-x^2)*(1-x^3)).
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%I #16 May 25 2024 22:55:15

%S 1,1,2,3,4,5,7,8,10,12,14,16,19,21,24,27,30,34,38,42,47,52,57,63,69,

%T 75,82,89,96,104,112,120,129,138,147,157,167,177,188,199,210,222,234,

%U 246,259,272,285,299,313

%N Expansion of (1+x^17)/((1-x)*(1-x^2)*(1-x^3)).

%H G. C. Greubel, <a href="/A008760/b008760.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 G.f.: (1+x^17)/((1-x)*(1-x^2)*(1-x^3)).

%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5). - _Wesley Ivan Hurt_, May 25 2024

%p seq(coeff(series((1+x^17)/((1-x)*(1-x^2)*(1-x^3)), x, n+1), x, n), n = 0 .. 60); # _G. C. Greubel_, Aug 09 2019

%t CoefficientList[Series[(1+x^17)/(1-x)/(1-x^2)/(1-x^3),{x,0,50}],x] (* _Harvey P. Dale_, Nov 30 2011 *)

%t Join[{1,1,2,3,4,5,7,8,10,12,14,16}, LinearRecurrence[{2,-1,1,-2,1}, {19, 21,24,27,30}, 48]] (* _G. C. Greubel_, Aug 09 2019 *)

%o (PARI) my(x='x+O('x^60)); Vec((1+x^17)/((1-x)*(1-x^2)*(1-x^3))) \\ _G. C. Greubel_, Aug 09 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^17)/((1-x)*(1-x^2)*(1-x^3)) )); // _G. C. Greubel_, Aug 09 2019

%o (Sage)

%o def A008760_list(prec):

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

%o return P( (1+x^17)/((1-x)*(1-x^2)*(1-x^3)) ).list()

%o A008760_list(60) # _G. C. Greubel_, Aug 09 2019

%o (GAP) a:=[19,21,24,27,30];; for n in [6..48] do a[n]:=2*a[n-1]-a[n-2] +a[n-3]-2*a[n-4]+a[n-5]; od; Concatenation([1,1,2,3,4,5,7,8,10,12,14, 16], a); # _G. C. Greubel_, Aug 09 2019

%K nonn

%O 0,3

%A _N. J. A. Sloane_