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%I #7 Mar 18 2023 03:56:03
%S 0,2,8,20,36,61,91,126,174,228,288,354,426,517,615,720,832,951,1077,
%T 1210,1350,1518,1694,1878,2070,2270,2478,2694,2918,3150,3390,3638,
%U 3894,4158,4464,4779,5103,5436,5778,6129,6489,6858,7236,7623,8019,8424,8838
%N Partial sums of A130237.
%H G. C. Greubel, <a href="/A130238/b130238.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) = Sum_{k=0..n} A130237(k).
%F a(n) = (n*(n+1)*A130233(n) - (Fib(A130233(n)) - 1)*(Fib(A130233(n) + 1) - 1))/2.
%F G.f.: (1/(1-x)^3)*Sum_{k>=1} (Fib(k)*(1-x) + x)*x^Fib(k).
%t a[n_]:= a[n]= Sum[j*Floor[Log[GoldenRatio, 3/2 +j*Sqrt[5]]], {j,0,n}];
%t Table[a[n], {n,0,70}] (* _G. C. Greubel_, Mar 18 2023 *)
%o (Magma) [(&+[j*Floor(Log(3/2 +j*Sqrt(5))/Log((1+Sqrt(5))/2)): j in [0..n]]): n in [0..70]]; // _G. C. Greubel_, Mar 18 2023
%o (SageMath)
%o def A130238(n): return sum(j*int(log(3/2 +j*sqrt(5), golden_ratio)) for j in range(n+1))
%o [A130238(n) for n in range(71)] # _G. C. Greubel_, Mar 18 2023
%Y Cf. A000045, A130233, A130234, A130235, A130236, A130237, A130239, A130240, A130243, A130246, A130248, A130239, A130251, A130253, A130257, A130261.
%K nonn
%O 0,2
%A _Hieronymus Fischer_, May 17 2007
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