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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A001622, A104457.

Cf. A004938 - A004955, A007067.

Programs

Magma

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

Mathematica

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

PARI

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

SageMath

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