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A130257
Partial sums of the 'lower' odd Fibonacci Inverse A130255.
12
1, 3, 5, 7, 10, 13, 16, 19, 22, 25, 28, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250
OFFSET
1,2
LINKS
FORMULA
a(n) = (n+1)*A130255(n) - A001906(A130255(n)).
a(n) = (n+1)*A130255(n) - Fib(2*A130255(n)).
G.f.: g(x)=1/(1-x)^2*sum(k>=1, x^Fib(2k-1)).
MATHEMATICA
Table[Sum[Floor[(1 + ArcSinh[Sqrt[5]*k/2]/Log[GoldenRatio])/2], {k, 1, n}], {n, 1, 100}] (* G. C. Greubel, Sep 09 2018 *)
PROG
(PARI) for(n=1, 100, print1(sum(k=1, n, floor((1+asinh(sqrt(5)*k/2)/log((1+sqrt(5))/2))/2)), ", ")) \\ G. C. Greubel, Sep 09 2018
(Magma) [(&+[Floor((1+Argsinh(Sqrt(5)*k/2)/Log((1+Sqrt(5))/2))/2): k in [1..n]]): n in [1..100]]; // G. C. Greubel, Sep 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, May 24 2007
STATUS
approved