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%I #6 Sep 08 2022 08:45:30
%S 1,2,4,7,10,13,17,21,25,29,34,39,44,49,54,59,64,70,76,82,88,94,100,
%T 106,112,118,124,130,137,144,151,158,165,172,179,186,193,200,207,214,
%U 221,228,235,242,249,256,264,272,280,288,296,304,312,320,328,336,344,352
%N Partial sums of the 'lower' Lucas Inverse A130241.
%H G. C. Greubel, <a href="/A130243/b130243.txt">Table of n, a(n) for n = 1..2500</a>
%F a(n) = Sum_{k=1..n} A130241(k).
%F a(n) = (n+1)*A130241(n) - A000032(A130241(n)+2) + 3.
%F G.f.: g(x) = 1/(1-x)^2*Sum_{k>=1} x^Lucas(k).
%t Table[1 + Sum[Floor[Log[GoldenRatio, k + 1/2]], {k, 1, n}], {n, 1, 50}] (* _G. C. Greubel_, Sep 13 2018 *)
%o (PARI) for(n=1,50, print1(1 + sum(k=1,n,floor(log(k+1/2)/log((1+sqrt(5))/2))), ", ")) \\ _G. C. Greubel_, Sep 13 2018
%o (Magma) [1 + (&+[Floor(Log(k+1/2)/Log((1+Sqrt(5))/2)): k in [1..n]]): n in [1..50]]; // _G. C. Greubel_, Sep 13 2018
%Y Other related sequences: A000032, A130244, A130242, A130245, A130246, A130248, A130251, A130257, A130261. Fibonacci inverse see A130233 - A130240, A104162.
%K nonn
%O 1,2
%A _Hieronymus Fischer_, May 19 2007