Kyle M. Zimmer - cp's OEIS frontend

User: Kyle M. Zimmer

Kyle M. Zimmer has authored 1 sequences.

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

Kyle M. Zimmer, Nov 12 2014

nonn

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.

Wikipedia, Triforce.
Kyle M. Zimmer, The Koch-Sierpinski Ninja Star.
Kyle M. Zimmer, Extra values.
Kyle M. Zimmer, Generate Sequences Src code.

Java
```
// See links.
```

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

cp's OEIS Frontend

User: Kyle M. Zimmer

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

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