A240734 a(n) = floor(6^n/(2+sqrt(5))^n).

1, 1, 2, 2, 4, 5, 8, 11, 16, 22, 32, 46, 65, 92, 130, 185, 262, 371, 526, 745, 1056, 1496, 2119, 3001, 4251, 6021, 8528, 12080, 17110, 24236, 34328, 48622, 68869, 97547, 138166, 195700, 277191, 392616, 556104, 787670, 1115663, 1580234, 2238256, 3170284

Offset: 0

Author

Kival Ngaokrajang, Apr 11 2014

Keywords

• nonn
• easy

Comments

a(n) is the perimeter (rounded down) of a decaflake after n iterations, let a(0) = 1. The total number of sides is 10*A000400(n). The total number of holes is A002275(n). 2 + sqrt(5) = A098317.

Links

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

Crossrefs

Cf. A000400, A002275, A098317, A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240735 (dodecaflake).

Programs

Maple

A240734:=n->floor(6^n/(2+sqrt(5))^n); seq(A240734(n), n=0..50); # Wesley Ivan Hurt, Apr 12 2014

Mathematica

Table[Floor[6^n/(2 + Sqrt[5])^n], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 12 2014 *)

PARI

{a(n)=floor(6^n/(2+sqrt(5))^n)}
       for (n=0, 100, print1(a(n), ", "))