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
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
PROG
See links.
CROSSREFS
KEYWORD
nonn
AUTHOR
Kyle M. Zimmer, Nov 12 2014
STATUS
approved