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A004937
a(n) = round(n*phi^2), where phi is the golden ratio, A001622.
4
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
0,2
LINKS
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
CROSSREFS
KEYWORD
nonn
STATUS
approved