|
%I #14 Apr 16 2014 13:53:49
%S 1,1,2,2,4,5,8,11,16,22,32,46,65,92,130,185,262,371,526,745,1056,1496,
%T 2119,3001,4251,6021,8528,12080,17110,24236,34328,48622,68869,97547,
%U 138166,195700,277191,392616,556104,787670,1115663,1580234,2238256,3170284
%N Floor(6^n/(2+sqrt(5))^n).
%C a(n) is the perimeter (rounded down) of a decaflake after n iterations, let a(0) = 1. The total number of sides is 10*A000400(n). The total number of holes is A002275(n). 2 + sqrt(5) = A098317.
%H Kival Ngaokrajang, <a href="/A240734/a240734.pdf">Illustration of decaflake for n = 0..3</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/N-flake">n-flake</a>
%p A240734:=n->floor(6^n/(2+sqrt(5))^n); seq(A240734(n), n=0..50); # _Wesley Ivan Hurt_, Apr 12 2014
%t Table[Floor[6^n/(2 + Sqrt[5])^n], {n, 0, 50}] (* _Wesley Ivan Hurt_, Apr 12 2014 *)
%o (PARI) {a(n)=floor(6^n/(2+sqrt(5))^n)}
%o for (n=0, 100, print1(a(n), ", "))
%Y Cf. A000400, A002275, A098317, A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240735 (dodecaflake).
%K nonn,easy
%O 0,3
%A _Kival Ngaokrajang_, Apr 11 2014
|
