A130257 - OEIS

A130257

Partial sums of the 'lower' odd Fibonacci Inverse A130255.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

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