A182798 Number of 4-colorings of the n X n X n triangular grid.

4, 24, 192, 2112, 32640, 718080, 22665216, 1031276544, 67849629696, 6468240187392, 894839431299072, 179851071814434816, 52561241074964496384, 22351071118387029737472, 13837189739906569661841408

Offset: 1

Author

Alois P. Heinz, Dec 02 2010

Keywords

• nonn

Comments

The n X n X n triangular grid has n rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The graph has A000217(n) vertices and 3*A000217(n-1) edges altogether.

Links

• Wikipedia, Chromatic polynomial
• Wikipedia, Triangular grid graph

Crossrefs

4th row of A182797. Cf. A178435, A182788, A182789, A182790, A182791, A182792, A182793, A182794, A182795, A182796.

Formula

a(n) = 4 * A153467(n).

Extensions

a(15) from Alois P. Heinz, Mar 11 2016