A130238 Partial sums of A130237.

0, 2, 8, 20, 36, 61, 91, 126, 174, 228, 288, 354, 426, 517, 615, 720, 832, 951, 1077, 1210, 1350, 1518, 1694, 1878, 2070, 2270, 2478, 2694, 2918, 3150, 3390, 3638, 3894, 4158, 4464, 4779, 5103, 5436, 5778, 6129, 6489, 6858, 7236, 7623, 8019, 8424, 8838

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

a(n) = Sum_{k=0..n} A130237(k).

a(n) = (n*(n+1)*A130233(n) - (Fib(A130233(n)) - 1)*(Fib(A130233(n) + 1) - 1))/2.

G.f.: (1/(1-x)^3)*Sum_{k>=1} (Fib(k)*(1-x) + x)*x^Fib(k).

Mathematica

a[n_]:= a[n]= Sum[j*Floor[Log[GoldenRatio, 3/2 +j*Sqrt[5]]], {j, 0, n}];
Table[a[n], {n, 0, 70}] (* G. C. Greubel, Mar 18 2023 *)

Prog

(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
(SageMath)
def A130238(n): return sum(j*int(log(3/2 +j*sqrt(5), golden_ratio)) for j in range(n+1))
[A130238(n) for n in range(71)] # G. C. Greubel, Mar 18 2023

Crossrefs

Cf. A000045, A130233, A130234, A130235, A130236, A130237, A130239, A130240, A130243, A130246, A130248, A130239, A130251, A130253, A130257, A130261.

Sequence in context: A071386 A031114 A327100 * A038460 A077588 A025219

Adjacent sequences: A130235 A130236 A130237 * A130239 A130240 A130241

Keyword

nonn

Author

Hieronymus Fischer, May 17 2007

Status

approved