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A117899 Expansion of (1 + 2*x + 5*x^2 + 3*x^3 + 2*x^4)/(1-x^3)^2.

%I A117899 #15 Sep 08 2022 08:45:24
%S A117899 1,2,5,5,6,10,9,10,15,13,14,20,17,18,25,21,22,30,25,26,35,29,30,40,33,
%T A117899 34,45,37,38,50,41,42,55,45,46,60,49,50,65,53,54,70,57,58,75,61,62,80,
%U A117899 65,66,85,69,70,90,73,74,95,77,78,100,81,82,105,85,86,110,89,90,115,93
%N A117899 Expansion of (1 + 2*x + 5*x^2 + 3*x^3 + 2*x^4)/(1-x^3)^2.
%C A117899 Row sums of A117898.
%H A117899 G. C. Greubel, <a href="/A117899/b117899.txt">Table of n, a(n) for n = 0..1000</a>
%H A117899 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F A117899 a(n) = 2*a(n-3) - a(n-6).
%F A117899 a(n) = Sum_{k=0..n} 2^abs(L(C(n,2)/3) - L(C(k,2)/3)), L(j/p) the Legendre symbol of j and p.
%t A117899 CoefficientList[Series[(1+2x+5x^2+3x^3+2x^4)/(1-x^3)^2,{x,0,90}],x] (* or *) LinearRecurrence[{0,0,2,0,0,-1},{1,2,5,5,6,10},90] (* _Harvey P. Dale_, Dec 18 2013 *)
%o A117899 (Magma) I:=[1,2,5,5,6,10]; [n le 6 select I[n] else 2*Self(n-3) - Self(n-6): n in [1..91]]; // _G. C. Greubel_, Oct 01 2021
%o A117899 (Sage)
%o A117899 def A117899_list(prec):
%o A117899     P.<x> = PowerSeriesRing(ZZ, prec)
%o A117899     return P( (1+2*x+5*x^2+3*x^3+2*x^4)/(1-x^3)^2 ).list()
%o A117899 A117899_list(90) # _G. C. Greubel_, Oct 01 2021
%Y A117899 Cf. A117898.
%K A117899 easy,nonn
%O A117899 0,2
%A A117899 _Paul Barry_, Apr 01 2006