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%I #17 Apr 15 2014 02:37:05
%S 1,1,2,3,5,8,13,21,32,50,78,121,187,289,448,693,1072,1658,2564,3966,
%T 6134,9487,14673,22695,35101,54288,83964,129862,200850,310643,480452,
%U 743085,1149282,1777523,2749182,4251987,6576279,10171116,15731022,24330178,37629950
%N Floor(6^n/(2+2*cos(Pi/9))^n).
%C a(n) is the perimeter (rounded down) of a nonaflake after n iterations, let a(0) = 1. The total number of sides is 9*A000400(n). The total number of holes is A002452(n). 2*cos(Pi/9) = 1.87938524... = diagonal b of nonagon (see comments in A123609).
%H Vincenzo Librandi, <a href="/A240733/b240733.txt">Table of n, a(n) for n = 0..1000</a>
%H Kival Ngaokrajang, <a href="/A240733/a240733_1.pdf">Illustration of nonaflake for n = 0..3</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/N-flake">n-flake</a>
%p A240733:=n->floor(6^n/(2+2*cos(Pi/9))^n); seq(A240733(n), n=0..50); # _Wesley Ivan Hurt_, Apr 12 2014
%t Table[Floor[6^n/(2 + 2*Cos[Pi/9])^n], {n, 0, 50}] (* _Wesley Ivan Hurt_, Apr 12 2014 *)
%o (PARI) {a(n)=floor(6^n/(2+2*cos(Pi/9))^n)}
%o for (n=0, 100, print1(a(n), ", "))
%Y Cf. A000400, A002452, A123609, A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240735 (dodecaflake).
%K nonn,easy
%O 0,3
%A _Kival Ngaokrajang_, Apr 11 2014
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