A240523 a(n) = floor(4^n/((1+sqrt(5))/2)^(2*n)).

1, 1, 2, 3, 5, 8, 12, 19, 29, 45, 69, 105, 161, 247, 377, 577, 881, 1347, 2058, 3144, 4805, 7341, 11216, 17137, 26183, 40005, 61122, 93387, 142682, 218000, 333074, 508892, 777518, 1187942, 1815014, 2773095, 4236913

Offset: 0

Author

Kival Ngaokrajang, Apr 07 2014

Keywords

• nonn
• easy

Comments

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).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Kival Ngaokrajang, Illustration for n = 0..4
• Eric Weisstein's World of Mathematics, Pentaflake
• Wikipedia, n-flake

Crossrefs

Cf. A000302, A000400, A113212.

Programs

Maple

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

Mathematica

Table[Floor[4^n/(((1 + Sqrt[5]))/2)^(2 n)], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 07 2014 *)
Table[Floor[4^n/GoldenRatio^(2n)],{n,0,40}] (* Harvey P. Dale, Mar 24 2018 *)

PARI

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

Formula

Equals floor((2/(phi))^(2*n)), where phi is the golden ratio. - G. C. Greubel, Jul 05 2017