A240840 - OEIS

%I #8 Apr 24 2014 09:52:49

%S 1,1,1,2,3,4,5,7,9,12,17,22,30,40,53,71,95,126,168,223,297,395,525,

%T 698,928,1234,1640,2180,2899,3854,5123,6811,9055,12038,16003,21275,

%U 28282,37599,49984,66448,88336,117433,156115

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

%C 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.

%H Kival Ngaokrajang, <a href="/A240840/a240840.pdf">Illustration of hendecaflake for n = 0..3</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/N-flake">n-flake</a>

%p 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

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

%o (PARI) {a(n)=floor(6^n/(1+1/(2*cos(5*Pi/11)))^n)}

%o        for (n=0, 100, print1(a(n), ", "))

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

%K nonn

%O 0,4

%A _Kival Ngaokrajang_, Apr 13 2014