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

0,3

Links

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

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).

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A186228 A184747 A361684 * A186496 A032765 A340931

Adjacent sequences: A130255 A130256 A130257 * A130259 A130260 A130261

Keyword

nonn

Author

Hieronymus Fischer, May 24 2007

Status

approved