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

0,2

Links

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

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).

Mathematica

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

Prog

(Magma) [n*Floor(Log(3/2 +n*Sqrt(5))/Log((1+Sqrt(5))/2)): n in [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

Crossrefs

Partial sums: A130238.

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

Sequence in context: A367465 A088915 A084790 * A053457 A299112 A154030

Adjacent sequences: A130234 A130235 A130236 * A130238 A130239 A130240

Keyword

nonn

Author

Hieronymus Fischer, May 17 2007

Status

approved