%I #6 Sep 08 2022 08:45:30

%S 0,0,2,5,8,11,15,19,23,27,31,35,39,43,48,53,58,63,68,73,78,83,88,93,

%T 98,103,108,113,118,123,128,133,138,143,148,154,160,166,172,178,184,

%U 190,196,202,208,214,220,226,232,238,244,250,256,262,268,274,280,286,292

%N Partial sums of the 'upper' odd Fibonacci Inverse A130256.

%H G. C. Greubel, <a href="/A130258/b130258.txt">Table of n, a(n) for n = 0..2500</a>

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

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

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

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

%o (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

%o (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

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

%K nonn

%O 0,3

%A _Hieronymus Fischer_, May 24 2007