A240572 a(n) = floor(4^n/(2 + sqrt(2))^n).

1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 9, 10, 12, 14, 17, 20, 23, 27, 32, 38, 44, 52, 61, 71, 84, 98, 115, 135, 158, 185, 217, 255, 299, 350, 410, 480, 563, 659, 773, 905, 1061, 1243, 1456, 1706, 1999, 2342, 2744, 3215, 3767, 4413, 5170, 6057, 7097, 8314

Offset: 0

Author

Kival Ngaokrajang, Apr 08 2014

Keywords

• nonn
• easy

Comments

a(n) is the perimeter (rounded down) of octaflake after n iterations, let a(0) = 1. The total number of sides is 8*A000302(n). The total number of holes is A084990(A000225(n)). sqrt(2) = A002193.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Kival Ngaokrajang, Illustration of octaflake for n = 0..3
• Wikipedia, n-flake

Crossrefs

Cf. A000302, A084990, A000225, A002193. A240523 (pentaflake), A240671 (heptaflake), A240733 (nonaflake), A240734 (decaflake), A230735 (dodecaflake).

Programs

Maple

A240572:=n->floor(4^n/(2 + sqrt(2))^n); seq(A240572(n), n=0..50); # Wesley Ivan Hurt, Apr 12 2014

Mathematica

Table[Floor[4^n/(2 + Sqrt[2])^n], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 12 2014 *)

PARI

{a(n)=floor(4^n/(2 + sqrt(2))^n)}
       for (n=0, 100, print1(a(n), ", "))