A130262 Partial sums of the 'upper' even Fibonacci Inverse A130260.

0, 1, 3, 5, 8, 11, 14, 17, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137, 142, 147, 152, 157, 162, 167, 172, 177, 182, 187, 192, 197, 202, 207, 212, 217, 222, 227, 232, 237, 242, 248, 254, 260, 266

Offset: 0

Author

Hieronymus Fischer, May 25 2007

Keywords

• nonn

Links

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

Crossrefs

Cf. A000045, A001519, A001906, A130234, A130235, A130236, A130256, A130259, A104161. Lucas inverse: A130241 - A130248.

Programs

Magma

[0] cat [(&+[ Ceiling(Log(Sqrt(5)*k)/(2*Log((1+ Sqrt(5))/2))): k in [1..n]]): n in [1..50]]; // G. C. Greubel, Sep 12 2018

Mathematica

Table[Sum[Ceiling[Log[GoldenRatio, Sqrt[5]*k]/2], {k, 1, n}], {n, 0, 60}] (* G. C. Greubel, Sep 12 2018 *)

PARI

for(n=0, 50, print1(sum(k=1,n, ceil(log(sqrt(5)*k)/(2*log((1+ sqrt(5))/2)))), ", ")) \\ G. C. Greubel, Sep 12 2018

Formula

a(n) = n*A130260(n) - A001519(A130260(n)) + 1.

a(n) = n*A130260(n) - Fib(2*A130260(n)-1) + 1.

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