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A130262 Partial sums of the 'upper' even Fibonacci Inverse A130260. 4
0, 1, 3, 5, 8, 11, 14, 17, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137, 142, 147, 152, 157, 162, 167, 172, 177, 182, 187, 192, 197, 202, 207, 212, 217, 222, 227, 232, 237, 242, 248, 254, 260, 266 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

FORMULA

a(n) = n*A130260(n) - A001519(A130260(n)) + 1.

a(n) = n*A130260(n) - Fib(2*A130260(n)-1) + 1.

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

MATHEMATICA

Table[Sum[Ceiling[Log[GoldenRatio, Sqrt[5]*k]/2], {k, 1, n}], {n, 0, 50}] (* G. C. Greubel, Sep 12 218 *)

PROG

(PARI) for(n=0, 50, print1(sum(k=1, n, ceil(log(sqrt(5)*k)/(2*log((1+ sqrt(5))/2)))), ", ")) \\ G. C. Greubel, Sep 12 2018

(MAGMA) [0] cat [(&+[ Ceiling(Log(Sqrt(5)*k)/(2*Log((1+ Sqrt(5))/2))): k in [1..n]]): n in [1..50]]; // G. C. Greubel, Sep 12 2018

CROSSREFS

Cf. A000045, A001519, A001906, A130234, A130235, A130236, A130256, A130259, A104161. Lucas inverse: A130241 - A130248.

Sequence in context: A084505 A084555 A102696 * A094228 A278586 A001855

Adjacent sequences:  A130259 A130260 A130261 * A130263 A130264 A130265

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 25 2007

STATUS

approved

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Last modified January 20 15:21 EST 2021. Contains 340302 sequences. (Running on oeis4.)