A004919 a(n) = floor(n*phi^4), where phi is the golden ratio, A001622.

0, 6, 13, 20, 27, 34, 41, 47, 54, 61, 68, 75, 82, 89, 95, 102, 109, 116, 123, 130, 137, 143, 150, 157, 164, 171, 178, 185, 191, 198, 205, 212, 219, 226, 233, 239, 246, 253, 260, 267, 274, 281, 287, 294, 301, 308

Offset

0,2

Comments

The golden section or golden ratio is now usually denoted by "phi", but it in the older literature it was more often denoted by "tau." - N. J. A. Sloane, Feb 17 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

A. J. Hildebrand, Junxian Li, Xiaomin Li, and Yun Xie, Almost Beatty Partitions, arXiv:1809.08690 [math.NT], 2018.

Index entries for sequences related to Beatty sequences

Formula

a(n) = 2*n + floor(3*n*tau). [Formula corrected by Charles R Greathouse IV, Mar 11 2011]

Mathematica

With[{c=GoldenRatio^4}, Floor[c*Range[0, 50]]] (* Harvey P. Dale, Apr 11 2012 *)

Prog

(Python)
from math import isqrt
def A004919(n): return (3*n+isqrt(45*n**2)>>1)+(n<<1) # Chai Wah Wu, Aug 17 2022
(Magma) [Floor((7+3*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Aug 22 2023
(SageMath) [floor(golden_ratio^4*n) for n in range(61)] # G. C. Greubel, Aug 22 2023

Crossrefs

Cf. A004920, A004921, A004922, A004923, A004924, A004925, A004926.

Cf. A004927, A004928, A004929, A004930, A004931, A004932, A004933.

Cf. A004934, A004935, A004976, A066096, A090909.

Cf. A000201, A001950.

Sequence in context: A337141 A043417 A031485 * A172330 A017053 A046040

Adjacent sequences: A004916 A004917 A004918 * A004920 A004921 A004922

Keyword

nonn

Author

N. J. A. Sloane

Status

approved