A004937 - OEIS

A004937

a(n) = round(n*phi^2), where phi is the golden ratio, A001622.

0, 3, 5, 8, 10, 13, 16, 18, 21, 24, 26, 29, 31, 34, 37, 39, 42, 45, 47, 50, 52, 55, 58, 60, 63, 65, 68, 71, 73, 76, 79, 81, 84, 86, 89, 92, 94, 97, 99, 102, 105, 107, 110, 113, 115, 118, 120, 123, 126, 128, 131, 134, 136, 139, 141, 144, 147, 149, 152, 154, 157

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000

Benoit Cloitre and Jeffrey Shallit, Some Fibonacci-Related Sequences, arXiv:2312.11706 [math.CO], 2023.

MATHEMATICA

a[n_] := Round[n*GoldenRatio^2]; Array[a, 50, 0] (* Amiram Eldar, Jun 17 2022 *)

PROG

(PARI) a(n)=round(n*(sqrt(5)+3)/2) \\ Charles R Greathouse IV, Aug 28 2016

(Magma) [Round((3+Sqrt(5))*n/2): n in [0..80]]; // G. C. Greubel, Sep 13 2023

(SageMath) [round(golden_ratio^2*n) for n in range(81)] # G. C. Greubel, Sep 13 2023