A166736 - OEIS

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 #24 May 30 2018 11:56:40

%S 3,24,528,31968,5332224,2450774016,3104112826368

%N 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 Project Euler, <a href="https://projecteuler.net/problem=189">Problem 189: Tri-colouring a triangular grid</a>

%e Illustration of first two rows:

%e /\

%e / \

%e / 1 \

%e / \

%e /________\

%e /\ /\

%e / \ / \

%e / 2 \ 3 / 4 \

%e / \ / \

%e /________\/________\

%e Triangles sharing a side are considered adjacent; e.g., 1 & 3 are adjacent in the figure, 1 & 2 are not.

%K nonn

%O 1,1

%A Chris Cole (chris(AT)questrel.com), Oct 20 2009

%E Edited by _Jon E. Schoenfield_, Jul 08 2017

%E Name simplified by _Charles R Greathouse IV_, Jul 09 2017