A240841 a(n) = floor(8^n/(1+2*sin(6*Pi/13)/(2*sin(Pi/13)))^n).

1, 1, 2, 3, 5, 9, 14, 21, 34, 52, 82, 127, 198, 308, 478, 744, 1156, 1796, 2792, 4339, 6742, 10477, 16282, 25302, 39318, 61100, 94947, 147545, 229281, 356295, 553672, 860388, 1337014, 2077676, 3228640, 5017200, 7796562, 12115600, 18827241, 29256909, 45464268

Offset: 0

Author

Kival Ngaokrajang, Apr 13 2014

Keywords

• nonn
• easy

Comments

a(n) is the perimeter (rounded down) of a tridecaflake after n iterations, let a(0) = 1. The total number of sides is 13*A001018(n). The total number of holes is A091030(n), n >= 1.

Links

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

Crossrefs

Cf. A001018, A091030, A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240840 (hendecaflake), A240735 (dodecaflake).

Programs

Maple

A240841:=n->floor(8^n/(1+2*sin(6*Pi/13)/(2*sin(Pi/13)))^n); seq(A240841(n), n=0..50); # Wesley Ivan Hurt, Apr 13 2014

Mathematica

Table[Floor[8^n/(1 + 2*Sin[6*Pi/13]/(2*Sin[Pi/13]))^n], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 13 2014 *)

PARI

{a(n)=floor(8^n/(1+2*sin(6*Pi/13)/(2*sin(Pi/13)))^n)}