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A130243 Partial sums of the 'lower' Lucas Inverse A130241. 10
1, 2, 4, 7, 10, 13, 17, 21, 25, 29, 34, 39, 44, 49, 54, 59, 64, 70, 76, 82, 88, 94, 100, 106, 112, 118, 124, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 221, 228, 235, 242, 249, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..2500

FORMULA

a(n) = Sum_{k=1..n} A130241(k).

a(n) = (n+1)*A130241(n) - A000032(A130241(n)+2) + 3.

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

MATHEMATICA

Table[1 + Sum[Floor[Log[GoldenRatio, k + 1/2]], {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Sep 13 2018 *)

PROG

(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

(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

CROSSREFS

Other related sequences: A000032, A130244, A130242, A130245, A130246, A130248, A130251, A130257, A130261. Fibonacci inverse see A130233 - A130240, A104162.

Sequence in context: A137281 A287420 A003067 * A061465 A126022 A194172

Adjacent sequences:  A130240 A130241 A130242 * A130244 A130245 A130246

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 19 2007

STATUS

approved

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Last modified July 28 09:10 EDT 2021. Contains 346322 sequences. (Running on oeis4.)