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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved