A240671 a(n) = floor(4^n/(2+2*cos(2*Pi/7))^n).

1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 15, 18, 22, 28, 34, 42, 52, 64, 79, 98, 121, 149, 183, 226, 279, 343, 423, 521, 642, 791, 975, 1201, 1480, 1823, 2246, 2767, 3409, 4199, 5173, 6373, 7851, 9672, 11915, 14679, 18083

Offset: 0

Author

Kival Ngaokrajang, Apr 10 2014

Keywords

• nonn
• easy

Comments

a(n) is the perimeter (rounded down) of a heptaflake after n iterations, let a(0) = 1. The total number of sides is 7*A000302(n). The total number of holes is A023000(n).

Links

• Kival Ngaokrajang, Illustration of heptaflake for n = 0..3
• Wikipedia, n-flake

Crossrefs

Cf. A000302, A023000, A116425, A240523 (pentaflake), A240572 (octaflake).

Programs

Maple

A240671:=n->floor(4^n/(2+2*cos(2*Pi/7))^n); seq(A240671(n), n=0..50); # Wesley Ivan Hurt, Apr 10 2014

Mathematica

Table[Floor[4^n/(2 + 2*Cos[2*Pi/7])^n], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 10 2014 *)

PARI

{a(n)=floor(4^n/(2+2*cos(2*Pi/7))^n)}
       for (n=0, 100, print1(a(n), ", "))

Formula

a(n) = floor(4^n/A116425(n)^n).