A130261 Partial sums of the 'lower' even Fibonacci Inverse A130259.

0, 1, 2, 4, 6, 8, 10, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 192, 197, 202, 207, 212, 217

Offset

0,3

Links

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

Formula

a(n) = (n+1)*A130259(n) - A001519(A130259(n)+1) + 1.

a(n) = (n+1)*A130259(n) - Fib(2*A130259(n)+1) + 1.

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

Mathematica

Table[Sum[Floor[1/2*Log[GoldenRatio, (Sqrt[5]*k + 1)]], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Sep 12 2018 *)

Prog

(PARI) for(n=0, 50, print1(sum(k=0, n, floor(log((sqrt(5)*k+1))/(2*log((1 +sqrt(5))/2)))), ", ")) \\ G. C. Greubel, Sep 12 2018
(Magma) [(&+[Floor(Log((Sqrt(5)*k+1))/(2*Log((1+Sqrt(5))/2))): k in [0..n]]): n in [0..50]]; // G. C. Greubel, Sep 12 2018

Crossrefs

Cf. A000045, A001519, A001906, A130233, A130235, A130236, A130255, A130257, A104162. Lucas inverse: A130241 - A130248.

Sequence in context: A248563 A278453 A347009 * A186384 A011860 A259278

Adjacent sequences: A130258 A130259 A130260 * A130262 A130263 A130264

Keyword

nonn

Author

Hieronymus Fischer, May 25 2007

Status

approved