A240523 - OEIS

%I #22 Mar 24 2018 14:24:35

%S 1,1,2,3,5,8,12,19,29,45,69,105,161,247,377,577,881,1347,2058,3144,

%T 4805,7341,11216,17137,26183,40005,61122,93387,142682,218000,333074,

%U 508892,777518,1187942,1815014,2773095,4236913

%N a(n) = floor(4^n/((1+sqrt(5))/2)^(2*n)).

%C a(n) is the perimeter (rounded down) of pentaflake after n iterations, let a(0) = 1. The total number of sides is 5*A000302(n).

%H G. C. Greubel, <a href="/A240523/b240523.txt">Table of n, a(n) for n = 0..1000</a>

%H Kival Ngaokrajang, <a href="/A240523/a240523.pdf">Illustration for n = 0..4</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pentaflake.html">Pentaflake</a>

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

%F Equals floor((2/(phi))^(2*n)), where phi is the golden ratio. - _G. C. Greubel_, Jul 05 2017

%p A240523:=n->floor(4^n/((1+sqrt(5))/2)^(2*n)); seq(A240523(n), n=0..50); # _Wesley Ivan Hurt_, Apr 07 2014

%t Table[Floor[4^n/(((1 + Sqrt[5]))/2)^(2 n)], {n, 0, 50}] (* _Wesley Ivan Hurt_, Apr 07 2014 *)

%t Table[Floor[4^n/GoldenRatio^(2n)],{n,0,40}] (* _Harvey P. Dale_, Mar 24 2018 *)

%o (PARI) a(n) = floor(4^n/((1+sqrt(5))/2)^(2*n))

%Y Cf. A000302, A000400, A113212.

%K nonn,easy

%O 0,3

%A _Kival Ngaokrajang_, Apr 07 2014