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A166736 Consider triangles stacked so the k-th row has 2*k-1 triangles. a(n) is the number of ways to color each triangle in the first n rows using three colors with the restriction that adjacent triangles must be different colors. (Triangles are adjacent if they share a side.)

%I A166736 #24 May 30 2018 11:56:40
%S A166736 3,24,528,31968,5332224,2450774016,3104112826368
%N A166736 Consider triangles stacked so the k-th row has 2*k-1 triangles. a(n) is the number of ways to color each triangle in the first n rows using three colors with the restriction that adjacent triangles must be different colors. (Triangles are adjacent if they share a side.)
%H A166736 Project Euler, <a href="https://projecteuler.net/problem=189">Problem 189: Tri-colouring a triangular grid</a>
%e A166736 Illustration of first two rows:
%e A166736            /\
%e A166736           /  \
%e A166736          /  1 \
%e A166736         /      \
%e A166736        /________\
%e A166736       /\        /\
%e A166736      /  \      /  \
%e A166736     /  2 \  3 /  4 \
%e A166736    /      \  /      \
%e A166736   /________\/________\
%e A166736 Triangles sharing a side are considered adjacent; e.g., 1 & 3 are adjacent in the figure, 1 & 2 are not.
%K A166736 nonn
%O A166736 1,1
%A A166736 Chris Cole (chris(AT)questrel.com), Oct 20 2009
%E A166736 Edited by _Jon E. Schoenfield_, Jul 08 2017
%E A166736 Name simplified by _Charles R Greathouse IV_, Jul 09 2017