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

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

(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

Cf. A000045, A001519, A001906, A130233, A130235, A130236, A130256, A130258, A104161. Lucas inverse: A130241 - A130248.

Sequence in context: A198409 A330072 A213510 * A276498 A186148 A079511

Adjacent sequences: A130254 A130255 A130256 * A130258 A130259 A130260

Keyword

nonn

Author

Hieronymus Fischer, May 24 2007

Status

approved