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%I A130257 #7 Sep 08 2022 08:45:30
%S A130257 1,3,5,7,10,13,16,19,22,25,28,31,35,39,43,47,51,55,59,63,67,71,75,79,
%T A130257 83,87,91,95,99,103,107,111,115,120,125,130,135,140,145,150,155,160,
%U A130257 165,170,175,180,185,190,195,200,205,210,215,220,225,230,235,240,245,250
%N A130257 Partial sums of the 'lower' odd Fibonacci Inverse A130255.
%H A130257 G. C. Greubel, <a href="/A130257/b130257.txt">Table of n, a(n) for n = 1..1000</a>
%F A130257 a(n) = (n+1)*A130255(n) - A001906(A130255(n)).
%F A130257 a(n) = (n+1)*A130255(n) - Fib(2*A130255(n)).
%F A130257 G.f.: g(x)=1/(1-x)^2*sum(k>=1, x^Fib(2k-1)).
%t A130257 Table[Sum[Floor[(1 + ArcSinh[Sqrt[5]*k/2]/Log[GoldenRatio])/2], {k, 1, n}], {n, 1, 100}] (* _G. C. Greubel_, Sep 09 2018 *)
%o A130257 (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
%o A130257 (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
%Y A130257 Cf. A000045, A001519, A001906, A130233, A130235, A130236, A130256, A130258, A104161. Lucas inverse: A130241 - A130248.
%K A130257 nonn
%O A130257 1,2
%A A130257 _Hieronymus Fischer_, May 24 2007

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