A223299 4 X 4 X 4 triangular graph coloring a rectangular array: number of n X 2 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

36, 324, 3132, 30564, 298620, 2918052, 28515132, 278649828, 2722966524, 26608833828, 260021573820, 2540931306084, 24829985481084, 242638664618916, 2371065485035068, 23170056359958756, 226417834139125500

Offset: 1

Author

R. H. Hardin, Mar 19 2013

Keywords

• nonn

Comments

Column 2 of A223305.

Examples

			Some solutions for n=3:
..0..2....2..0....8..9....5..4....7..8....0..2....4..8....3..4....3..4....1..3
..2..5....4..1....4..5....9..8....4..7....1..0....2..5....4..2....1..2....0..1
..5..2....1..2....1..4....5..9....7..3....0..2....1..2....8..4....2..1....1..3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A223305.

Formula

Empirical: a(n) = 11*a(n-1) - 12*a(n-2).

Conjectures from Colin Barker, Aug 19 2018: (Start)

G.f.: 36*x*(1 - 2*x) / (1 - 11*x + 12*x^2).

a(n) = (3*2^(-n)*((11-sqrt(73))^n*(-1+sqrt(73)) + (1+sqrt(73))*(11+sqrt(73))^n)) / sqrt(73).

(End)