A054088 a(n) = A054086(3n); also a bisection of A003511.

2, 5, 8, 10, 13, 16, 19, 21, 24, 27, 30, 32, 35, 38, 40, 43, 46, 49, 51, 54, 57, 60, 62, 65, 68, 71, 73, 76, 79, 81, 84, 87, 90, 92, 95, 98, 101, 103, 106, 109, 112, 114, 117, 120, 122, 125, 128, 131, 133, 136, 139, 142, 144, 147, 150

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Crossrefs

Cf. A003511, A022838, A054086.

Programs

Magma

[3*Floor(n*(Sqrt(3)-1))+2*Floor(n*(2-Sqrt(3)))+2: n in [1..60]]; // Vincenzo Librandi, Dec 18 2016

Maple

A054088 := proc(n) floor(n*(1+sqrt(3))) ; end proc: # R. J. Mathar, Feb 26 2011

Mathematica

Table[Floor[n (1 + Sqrt[3])], {n, 100}] (* Wesley Ivan Hurt, Dec 17 2016 *)

Formula

a(n) = floor( n*(1+sqrt(3)) ) = n + floor(n*sqrt(3)). - R. J. Mathar, Feb 26 2011

a(n) = n + A022838(n). - R. J. Mathar, Jan 25 2015

From Miko Labalan, Dec 17 2016: (Start)

For n > 0, a(n) = 3*floor(n*(sqrt(3)-1)) + 2*floor(n*(2-sqrt(3))) + 2;

a(0) = 0, a(n) = a(n - 1) + A022838(n) - A022838(n - 1) + 1. (End)

Extensions

A-number in the definition corrected by R. J. Mathar, Oct 05 2008