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%I #17 Sep 08 2022 08:45:30
%S 0,1,3,6,10,14,18,23,28,33,38,44,50,56,62,68,74,80,87,94,101,108,115,
%T 122,129,136,143,150,157,165,173,181,189,197,205,213,221,229,237,245,
%U 253,261,269,277,285,293,301,310,319,328,337,346,355,364,373,382,391
%N Partial sums of A130245.
%H G. C. Greubel, <a href="/A130246/b130246.txt">Table of n, a(n) for n = 0..2500</a>
%F a(n) = Sum_{k=1..n} A130245(k).
%F a(n) = 1 +(n+1)*A130245(n) - A000032(A130245(n)+1) for n=0 or n >= 2.
%F G.f.: 1/(1-x)^2*Sum_{k>=0} x^A000032(k).
%t Table[Sum[1 + Floor[Log[GoldenRatio, (2*k + 1)/2]], {k, 1, n}], {n, 0, 100}] (* _G. C. Greubel_, Sep 09 2018 *)
%o (PARI) for(n=0, 100, print1(sum(k=1,n, 1 + floor(log((2*k+1)/2)/log((1+sqrt(5))/2))), ", ")) \\ _G. C. Greubel_, Sep 09 2018
%o (Magma) [0] cat [(&+[1+Floor(Log((2*k+1)/2)/Log((1+Sqrt(5))/2)): k in [1..n]]): n in [1..100]]; // _G. C. Greubel_, Sep 09 2018
%Y Other related sequences: A000032, A130241, A130243, A130244, A130248, A130251, A130252, A130255, A130257, A130261. Fibonacci inverse see A130233 - A130240, A104162.
%K nonn
%O 0,3
%A _Hieronymus Fischer_, May 19 2007
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