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%I #14 Apr 13 2014 11:27:47
%S 1,1,1,2,2,3,4,5,6,8,10,13,17,21,27,35,44,56,71,90,115,146,185,235,
%T 298,378,479,607,770,977,1238,1570,1991,2525,3202,4060,5148,6527,8276,
%U 10494,13306,16872,21393,27125,34393,43609,55294,70111,88897,112717,142919
%N Floor(6^n/(3+sqrt(3))^n).
%C a(n) is the perimeter (rounded down) of a dodecaflake after n iterations, let a(0) = 1. The total number of sides is 12*A000400(n). The total number of holes is A240846. 3 + sqrt(3) = A165663.
%H Kival Ngaokrajang, <a href="/A240735/a240735_1.pdf">Illustration of dodecaflake for n = 0..3</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/N-flake">n-flake</a>
%p A240735:=n->floor(6^n/(3+sqrt(3))^n); seq(A240735(n), n=0..50); # _Wesley Ivan Hurt_, Apr 12 2014
%t Table[Floor[6^n/(3 + Sqrt[3])^n], {n, 0, 50}] (* _Wesley Ivan Hurt_, Apr 12 2014 *)
%o (PARI) {a(n)=floor(6^n/(3+sqrt(3))^n)}
%o for (n=0, 100, print1(a(n), ", "))
%Y Cf. A000400, A240846, A165663, A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240735 (dodecaflake).
%K nonn,easy
%O 0,4
%A _Kival Ngaokrajang_, Apr 11 2014
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