A250128 Number of triforces generated at iteration n in a Koch-Sierpiński Ninja Star.

0, 1, 3, 9, 30, 96, 309, 996, 3207, 10329, 33267, 107142, 345072, 1111371, 3579384, 11528097, 37128459, 119579361, 385128390, 1240380240, 3994883733

Offset

0,3

Comments

This sequence describes the number of triangles produced in each iteration of the fractal that is generated by nesting two-dimensional trees of valency three inside one another geometrically.

Links

Table of n, a(n) for n=0..20.

Wikipedia, Triforce.

Kyle M. Zimmer, The Koch-Sierpinski Ninja Star.

Kyle M. Zimmer, Extra values.

Kyle M. Zimmer, Generate Sequences Src code.

Formula

Refer to the blog link.

Conjecture: a(n) = 2*a(n-1) + 3*a(n-2) + 3*a(n-3). - Colin Barker, Nov 13 2014

Empirical g.f.: -x*(x+1) / (3*x^3 + 3*x^2 + 2*x - 1). - Colin Barker, Nov 13 2014

Empirical: a(n) = A077832(n-2) + A077832(n-1). - R. J. Mathar, May 21 2018

Prog

See links.

Crossrefs

Sequence in context: A144817 A337267 A337034 * A199137 A089978 A052906

Adjacent sequences: A250125 A250126 A250127 * A250129 A250130 A250131

Keyword

nonn

Author

Kyle M. Zimmer, Nov 12 2014

Status

approved