%I #50 Aug 23 2023 12:20:28

%S 0,6,13,20,27,34,41,47,54,61,68,75,82,89,95,102,109,116,123,130,137,

%T 143,150,157,164,171,178,185,191,198,205,212,219,226,233,239,246,253,

%U 260,267,274,281,287,294,301,308

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

%C 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

%H Vincenzo Librandi, <a href="/A004919/b004919.txt">Table of n, a(n) for n = 0..1000</a>

%H A. J. Hildebrand, Junxian Li, Xiaomin Li, and Yun Xie, <a href="https://arxiv.org/abs/1809.08690">Almost Beatty Partitions</a>, arXiv:1809.08690 [math.NT], 2018.

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

%F a(n) = 2*n + floor(3*n*tau). [Formula corrected by _Charles R Greathouse IV_, Mar 11 2011]

%t With[{c=GoldenRatio^4},Floor[c*Range[0,50]]] (* _Harvey P. Dale_, Apr 11 2012 *)

%o (Python)

%o from math import isqrt

%o def A004919(n): return (3*n+isqrt(45*n**2)>>1)+(n<<1) # _Chai Wah Wu_, Aug 17 2022

%o (Magma) [Floor((7+3*Sqrt(5))*n/2): n in [0..60]]; // _G. C. Greubel_, Aug 22 2023

%o (SageMath) [floor(golden_ratio^4*n) for n in range(61)] # _G. C. Greubel_, Aug 22 2023

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

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

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

%Y Cf. A000201, A001950.

%K nonn

%O 0,2

%A _N. J. A. Sloane_