A240735 a(n) = floor(6^n/(3+sqrt(3))^n).

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 13, 17, 21, 27, 35, 44, 56, 71, 90, 115, 146, 185, 235, 298, 378, 479, 607, 770, 977, 1238, 1570, 1991, 2525, 3202, 4060, 5148, 6527, 8276, 10494, 13306, 16872, 21393, 27125, 34393, 43609, 55294, 70111, 88897, 112717, 142919

Offset: 0

Author

Kival Ngaokrajang, Apr 11 2014

Keywords

• nonn
• easy

Comments

a(n) is the perimeter (rounded down) of a dodecaflake after n iterations, let a(0) = 1. The total number of sides is 12*A000400(n). The total number of holes is A240846. 3 + sqrt(3) = A165663.

Links

• Kival Ngaokrajang, Illustration of dodecaflake for n = 0..3
• Wikipedia, n-flake

Crossrefs

Cf. A000400, A240846, A165663, A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240735 (dodecaflake).

Programs

Maple

A240735:=n->floor(6^n/(3+sqrt(3))^n); seq(A240735(n), n=0..50); # Wesley Ivan Hurt, Apr 12 2014

Mathematica

Table[Floor[6^n/(3 + Sqrt[3])^n], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 12 2014 *)

PARI

{a(n)=floor(6^n/(3+sqrt(3))^n)}
       for (n=0, 100, print1(a(n), ", "))