A256429 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.

1, 6, 11, 16, 41, 106, 211, 416, 941, 2106, 4411, 9316, 20341, 44106, 94111, 201716, 435741, 938606, 2014311, 4330116, 9324641, 20060606, 43122511, 92747016, 199552041, 429222606, 923076211, 1985467416, 4270895441, 9186237106, 19758020411, 42498043816, 91411232341

Offset: 0

Author

Kival Ngaokrajang, Mar 28 2015

Keywords

• nonn

Comments

Inspired by A255870. But at the higher iterations, the perimeter would be a pentagram instead of a pentagon. See illustration in the links.

Links

• Kival Ngaokrajang, Illustration of initial terms, Illustration of n = 6

Crossrefs

Cf. A255870.

Formula

Conjectures from Colin Barker, Mar 29 2015: (Start)

a(n) = 3*a(n-1)-4*a(n-2)+7*a(n-3)-5*a(n-4) for n>3.

G.f.: -(3*x^2-3*x-1) / ((x-1)*(5*x^3-2*x^2+2*x-1)).

(End)