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A130246 Partial sums of A130245. 11
0, 1, 3, 6, 10, 14, 18, 23, 28, 33, 38, 44, 50, 56, 62, 68, 74, 80, 87, 94, 101, 108, 115, 122, 129, 136, 143, 150, 157, 165, 173, 181, 189, 197, 205, 213, 221, 229, 237, 245, 253, 261, 269, 277, 285, 293, 301, 310, 319, 328, 337, 346, 355, 364, 373, 382, 391 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

FORMULA

a(n) = Sum_{k=1..n} A130245(k).

a(n) = 1 +(n+1)*A130245(n) - A000032(A130245(n)+1) for n=0 or n >= 2.

G.f.: 1/(1-x)^2*Sum_{k>=0} x^A000032(k).

MATHEMATICA

Table[Sum[1 + Floor[Log[GoldenRatio, (2*k + 1)/2]], {k, 1, n}], {n, 0, 100}] (* G. C. Greubel, Sep 09 2018 *)

PROG

(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

(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

CROSSREFS

Other related sequences: A000032, A130241, A130243, A130244, A130248, A130251, A130252, A130255, A130257, A130261. Fibonacci inverse see A130233 - A130240, A104162.

Sequence in context: A310064 A113127 A145913 * A167381 A269745 A310065

Adjacent sequences:  A130243 A130244 A130245 * A130247 A130248 A130249

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 19 2007

STATUS

approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)