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URL: https://oeis.org/A130238

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A130238
Partial sums of A130237.
6
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
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
(Python)
def A130238(n):
a, b, c = 0, 1, 0
while b <= n:
c += 1
a, b = b, a+b
return n*(n+1)*c-(a-1)*(b-1)>>1 # Chai Wah Wu, Sep 07 2025
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, May 17 2007
STATUS
approved