A130237 The 'lower' Fibonacci Inverse A130233(n) multiplied by n.

0, 2, 6, 12, 16, 25, 30, 35, 48, 54, 60, 66, 72, 91, 98, 105, 112, 119, 126, 133, 140, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477, 486, 550

Offset: 0

Author

Hieronymus Fischer, May 17 2007

Keywords

• nonn

Links

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

Crossrefs

Partial sums: A130238.

Cf. A000045, A130233, A130234, A130235, A130236, A130238, A130239, A130240, A130243, A130246, A130248, A130239, A130251, A130253, A130257, A130261.

Programs

Magma

[n*Floor(Log(3/2 +n*Sqrt(5))/Log((1+Sqrt(5))/2)): n in [0..70]]; // G. C. Greubel, Mar 18 2023

Mathematica

Table[n*Floor[Log[GoldenRatio, 3/2 +n*Sqrt[5]]], {n,0,70}] (* G. C. Greubel, Mar 18 2023 *)

SageMath

[n*int(log(3/2 +n*sqrt(5), golden_ratio)) for n in range(71)] # G. C. Greubel, Mar 18 2023

Formula

a(n) = n*A130233(n).

a(n) = n*floor(arcsinh(sqrt(5)*n/2)/log(phi)).

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