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a(n) = floor(n*tau^3) where tau is the tribonacci constant (A058265).
8

%I #25 Apr 12 2019 05:19:58

%S 0,6,12,18,24,31,37,43,49,56,62,68,74,80,87,93,99,105,112,118,124,130,

%T 136,143,149,155,161,168,174,180,186,192,199,205,211,217,224,230,236,

%U 242,248,255,261,267,273,280,286,292,298,304,311,317,323,329,336,342,348,354,360,367,373,379,385

%N a(n) = floor(n*tau^3) where tau is the tribonacci constant (A058265).

%H Jon E. Schoenfield, <a href="/A277723/b277723.txt">Table of n, a(n) for n = 0..10000</a>

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

%F By definition, a(n) = n*tau^3 + O(1). - _Charles R Greathouse IV_, Nov 06 2016

%o (PARI) a(n)=n*polrootsreal(x^3-7*x^2+5*x-1)[1]\1 \\ _Charles R Greathouse IV_, Nov 06 2016

%Y Cf. A058265, A158919, A276801, A277722.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Oct 30 2016