A233251 Number of n X 3 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

3, 104, 4672, 221696, 10620928, 509640704, 24461443072, 1174138781696, 56358577635328, 2705211055407104, 129850125290831872, 6232805971010256896, 299174686264894947328, 14360384937966178402304, 689298477000386330755072

Offset: 1

Author

R. H. Hardin, Dec 06 2013

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A233256.

Formula

Empirical: a(n) = 56*a(n-1) - 384*a(n-2).

Conjectures from Colin Barker, Oct 10 2018: (Start)

G.f.: x*(3 - 64*x) / ((1 - 8*x)*(1 - 48*x)).

a(n) = 8^(n-1) * (6^n+3) / 3.

(End)