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a(n) = floor(n*tau^2) where tau is the tribonacci constant (A058265).
9

%I #29 Jan 18 2022 05:23:36

%S 0,3,6,10,13,16,20,23,27,30,33,37,40,43,47,50,54,57,60,64,67,71,74,77,

%T 81,84,87,91,94,98,101,104,108,111,115,118,121,125,128,131,135,138,

%U 142,145,148,152,155,158,162,165,169,172,175,179,182,186,189,192,196,199,202,206,209,213,216,219

%N a(n) = floor(n*tau^2) where tau is the tribonacci constant (A058265).

%H JungHwan Min, <a href="/A277722/b277722.txt">Table of n, a(n) for n = 0..10000</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.

%p A277722 := proc(n)

%p a276800 := 3.3829757679062374941227085364550345869493820437485761820195626772353718960099402922235933340043661396041006 ;

%p floor(n*a276800) ;

%p end proc:

%p seq(A277722(n),n=0..100) ; # _R. J. Mathar_, Nov 02 2016

%t A277722[n_] := Floor[n (1/3 (1 + (19 - 3 Sqrt[33])^(1/3) + (19 + 3 Sqrt[33])^(1/3)))^2]; Array[A277722, 66, 0] (* _JungHwan Min_, Nov 06 2016 *)

%Y Cf. A058265, A158919, A276800, A277723.

%K nonn

%O 0,2

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