A130258 Partial sums of the 'upper' odd Fibonacci Inverse A130256.

0, 0, 2, 5, 8, 11, 15, 19, 23, 27, 31, 35, 39, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 154, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274, 280, 286, 292

Offset: 0

Author

Hieronymus Fischer, May 24 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500

Crossrefs

Cf. A000045, A001519, A001906, A130234, A130235, A130236, A130255, A130257, A104162. Lucas inverse: A130241 - A130248.

Programs

Magma

[0,0] cat [(&+[Ceiling((1/2)*(1 + Log(Sqrt(5)*k-1)/Log((1+Sqrt(5))/2))): k in [2..n]]): n in [2..50]]; // G. C. Greubel, Sep 13 2018

Mathematica

Table[Sum[Ceiling[1/2*(1 + Log[GoldenRatio, (Sqrt[5]*k - 1)])], {k,2,n}], {n, 0, 50}] (* G. C. Greubel, Sep 13 2018 *)

PARI

for(n=0, 50, print1(if(n==0, 0, if(n==1, 0, sum(k=2, n, ceil( (1/2)*(1 + log(sqrt(5)*k - 1)/log((1+sqrt(5))/2)))))), ", ")) \\ G. C. Greubel, Sep 13 2018

Formula

a(n) = n*A130256(n) - A001906(A130256(n) -1).

a(n) = n*A130256(n) - Fib(2*A130256(n)-2) - 1.

G.f.: g(x) = x/(1-x)^2*Sum_{k>=0} x^Fib(2*k-1).