A240733 a(n) = floor(6^n/(2+2*cos(Pi/9))^n).

1, 1, 2, 3, 5, 8, 13, 21, 32, 50, 78, 121, 187, 289, 448, 693, 1072, 1658, 2564, 3966, 6134, 9487, 14673, 22695, 35101, 54288, 83964, 129862, 200850, 310643, 480452, 743085, 1149282, 1777523, 2749182, 4251987, 6576279, 10171116, 15731022, 24330178, 37629950

Offset: 0

Author

Kival Ngaokrajang, Apr 11 2014

Keywords

• nonn
• easy

Comments

a(n) is the perimeter (rounded down) of a nonaflake after n iterations, let a(0) = 1. The total number of sides is 9*A000400(n). The total number of holes is A002452(n). 2*cos(Pi/9) = 1.87938524... = diagonal b of nonagon (see comments in A123609).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Kival Ngaokrajang, Illustration of nonaflake for n = 0..3
• Wikipedia, n-flake

Crossrefs

Cf. A000400, A002452, A123609, A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240735 (dodecaflake).

Programs

Maple

A240733:=n->floor(6^n/(2+2*cos(Pi/9))^n); seq(A240733(n), n=0..50); # Wesley Ivan Hurt, Apr 12 2014

Mathematica

Table[Floor[6^n/(2 + 2*Cos[Pi/9])^n], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 12 2014 *)

PARI

{a(n)=floor(6^n/(2+2*cos(Pi/9))^n)}
       for (n=0, 100, print1(a(n), ", "))