%I #10 Sep 08 2022 08:45:30

%S 0,1,2,4,6,8,10,12,15,18,21,24,27,30,33,36,39,42,45,48,51,55,59,63,67,

%T 71,75,79,83,87,91,95,99,103,107,111,115,119,123,127,131,135,139,143,

%U 147,151,155,159,163,167,171,175,179,183,187,192,197,202,207,212,217

%N Partial sums of the 'lower' even Fibonacci Inverse A130259.

%H G. C. Greubel, <a href="/A130261/b130261.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) = (n+1)*A130259(n) - A001519(A130259(n)+1) + 1.

%F a(n) = (n+1)*A130259(n) - Fib(2*A130259(n)+1) + 1.

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

%t Table[Sum[Floor[1/2*Log[GoldenRatio, (Sqrt[5]*k + 1)]], {k, 0, n}], {n, 0, 50}] (* _G. C. Greubel_, Sep 12 2018 *)

%o (PARI) for(n=0,50, print1(sum(k=0,n, floor(log((sqrt(5)*k+1))/(2*log((1 +sqrt(5))/2)))), ", ")) \\ _G. C. Greubel_, Sep 12 2018

%o (Magma) [(&+[Floor(Log((Sqrt(5)*k+1))/(2*Log((1+Sqrt(5))/2))): k in [0..n]]): n in [0..50]]; // _G. C. Greubel_, Sep 12 2018

%Y Cf. A000045, A001519, A001906, A130233, A130235, A130236, A130255, A130257, A104162. Lucas inverse: A130241 - A130248.

%K nonn

%O 0,3

%A _Hieronymus Fischer_, May 25 2007