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.)

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

Offset: 1

Author

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

Keywords

• nonn

Examples

			Illustration of first two rows:
           /\
          /  \
         /  1 \
        /      \
       /________\
      /\        /\
     /  \      /  \
    /  2 \  3 /  4 \
   /      \  /      \
  /________\/________\
Triangles sharing a side are considered adjacent; e.g., 1 & 3 are adjacent in the figure, 1 & 2 are not.
		

Links

• Project Euler, Problem 189: Tri-colouring a triangular grid

Extensions

Edited by Jon E. Schoenfield, Jul 08 2017

Name simplified by Charles R Greathouse IV, Jul 09 2017