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%I #12 Feb 26 2024 19:16:33
%S 0,0,4,8,16,14,16,18,24,30,30,30,34,38,46,44,46,48,54,60,60,60,64,68,
%T 76,74,76,78,84,90,90,90,94,98,106,104,106,108,114,120,120,120,124,
%U 128,136,134,136,138,144,150,150,150,154,158,166,164,166,168,174,180,180,180
%N Partial sums of A137797.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,1,0,-1).
%F f(n) = Sum{k=0,n} 2*((k+1) mod 5) - 2*((k+1) mod 2).
%F a(n) = a(n-2)+a(n-5)-a(n-7) for n>6. - _Colin Barker_, Dec 16 2014
%F G.f.: 2*x^2*(3*x^3+6*x^2+4*x+2) / ((x-1)^2*(x+1)*(x^4+x^3+x^2+x+1)). - _Colin Barker_, Dec 16 2014
%t Accumulate[LinearRecurrence[{-1,0,0,0,1,1},{0,0,4,4,8,-2,2},100]] (* or *) LinearRecurrence[{0,1,0,0,1,0,-1},{0,0,4,8,16,14,16},100] (* _Harvey P. Dale_, Jun 08 2015 *)
%o (Python)
%o sequence = []
%o l = list(range(20))
%o while len(l) > 0:
%o a = l.pop(0)
%o z = sum(2*((x+1)%5)-2*((x+1)%2) for x in range(a))
%o sequence.append(z)
%o print(sequence)
%o (PARI) concat([0,0], Vec(2*x^2*(3*x^3+6*x^2+4*x+2)/((x-1)^2*(x+1)*(x^4+x^3+x^2+x+1)) + O(x^100))) \\ _Colin Barker_, Dec 16 2014
%Y Cf. A137797.
%K easy,nonn
%O 0,3
%A _William A. Tedeschi_, Feb 10 2008
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