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%I #34 Jan 16 2022 23:32:57
%S 0,1,3,9,30,96,309,996,3207,10329,33267,107142,345072,1111371,3579384,
%T 11528097,37128459,119579361,385128390,1240380240,3994883733
%N Number of triforces generated at iteration n in a Koch-Sierpiński Ninja Star.
%C 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.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Triforce">Triforce</a>.
%H Kyle M. Zimmer, <a href="http://mokaimath.blogspot.com/2014/04/the-koch-sierpinski-ninja-star.html">The Koch-Sierpinski Ninja Star</a>.
%H Kyle M. Zimmer, <a href="/A250128/a250128.txt">Extra values</a>.
%H Kyle M. Zimmer, <a href="/A250128/a250128_1.java.txt">Generate Sequences Src code</a>.
%F Refer to the blog link.
%F Conjecture: a(n) = 2*a(n-1) + 3*a(n-2) + 3*a(n-3). - _Colin Barker_, Nov 13 2014
%F Empirical g.f.: -x*(x+1) / (3*x^3 + 3*x^2 + 2*x - 1). - _Colin Barker_, Nov 13 2014
%F Empirical: a(n) = A077832(n-2) + A077832(n-1). - _R. J. Mathar_, May 21 2018
%o See links.
%K nonn
%O 0,3
%A _Kyle M. Zimmer_, Nov 12 2014
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