A240840 Floor(6^n/(1+1/(2*cos(5*Pi/11)))^n).

1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 17, 22, 30, 40, 53, 71, 95, 126, 168, 223, 297, 395, 525, 698, 928, 1234, 1640, 2180, 2899, 3854, 5123, 6811, 9055, 12038, 16003, 21275, 28282, 37599, 49984, 66448, 88336, 117433, 156115

Offset: 0

Author

Kival Ngaokrajang, Apr 13 2014

Keywords

• nonn

Comments

a(n) is the perimeter (rounded down) of a hendecaflake after n iterations, let a(0) = 1. The total number of sides is 11*A000400(n). The total number of holes is A016123(n), n >=1. 1/(2*cos(5*Pi/11)) = A231186.

Links

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

Crossrefs

Cf. A000400, A016123, A231186, A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240735 (dodecaflake), A240841 (tridecaflake).

Programs

Maple

A240840:=n->floor(6^n/(1+1/(2*cos(5*Pi/11)))^n); seq(A240840(n), n=0..50); # Wesley Ivan Hurt, Apr 13 2014

Mathematica

Table[Floor[6^n/(1 + 1/(2*Cos[5*Pi/11]))^n], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 13 2014 *)

PARI

{a(n)=floor(6^n/(1+1/(2*cos(5*Pi/11)))^n)}
       for (n=0, 100, print1(a(n), ", "))