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%I #10 Sep 08 2022 08:45:30
%S 0,1,3,5,8,11,14,17,20,24,28,32,36,40,44,48,52,56,60,64,68,72,77,82,
%T 87,92,97,102,107,112,117,122,127,132,137,142,147,152,157,162,167,172,
%U 177,182,187,192,197,202,207,212,217,222,227,232,237,242,248,254,260,266
%N Partial sums of the 'upper' even Fibonacci Inverse A130260.
%H G. C. Greubel, <a href="/A130262/b130262.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) = n*A130260(n) - A001519(A130260(n)) + 1.
%F a(n) = n*A130260(n) - Fib(2*A130260(n)-1) + 1.
%F G.f.: g(x)=x/(1-x)^2*Sum_{k>=0} x^Fib(2*k).
%t Table[Sum[Ceiling[Log[GoldenRatio, Sqrt[5]*k]/2], {k, 1, n}], {n, 0, 50}] (* _G. C. Greubel_, Sep 12 218 *)
%o (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
%o (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
%Y Cf. A000045, A001519, A001906, A130234, A130235, A130236, A130256, A130259, A104161. Lucas inverse: A130241 - A130248.
%K nonn
%O 0,3
%A _Hieronymus Fischer_, May 25 2007
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