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Expansion of (1+x^16)/(1-x)/(1-x^2)/(1-x^3).
1

%I #13 Sep 08 2022 08:44:36

%S 1,1,2,3,4,5,7,8,10,12,14,16,19,21,24,27,31,34,39,43,48,53,59,64,71,

%T 77,84,91,99,106,115,123,132,141,151,160,171,181,192,203,215,226,239,

%U 251,264,277,291,304,319

%N Expansion of (1+x^16)/(1-x)/(1-x^2)/(1-x^3).

%H G. C. Greubel, <a href="/A008759/b008759.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).

%p seq(coeff(series((1+x^16)/((1-x)*(1-x^2)*(1-x^3)), x, n+1), x, n), n = 1 .. 60); # _G. C. Greubel_, Aug 09 2019

%t CoefficientList[Series[(1+x^16)/(1-x)/(1-x^2)/(1-x^3),{x,0,60}],x] (* _Harvey P. Dale_, Sep 19 2016 *)

%t Join[{1,1,2,3,4,5,7,8,10,12,14}, LinearRecurrence[{1,1,0,-1,-1,1}, {16, 19,21,24,27,31}, 48]] (* _G. C. Greubel_, Aug 09 2019 *)

%o (PARI) my(x='x+O('x^60)); Vec((1+x^16)/((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^16)/((1-x)*(1-x^2)*(1-x^3)) )); // _G. C. Greubel_, Aug 09 2019

%o (Sage)

%o def A008759_list(prec):

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

%o return P( (1+x^16)/((1-x)*(1-x^2)*(1-x^3)) ).list()

%o A008759_list(60) # _G. C. Greubel_, Aug 09 2019

%o (GAP) a:=[16,19,21,24,27,31];; for n in [7..60] do a[n]:=a[n-1]+a[n-2]-a[n-4] -a[n-5]+a[n-6]; od; Concatenation([1,1,2,3,4,5,7,8,10,12,14], a); # _G. C. Greubel_, Aug 09 2019

%K nonn

%O 0,3

%A _N. J. A. Sloane_