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

1,1

Links

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

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)

Example

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

Crossrefs

Column 3 of A233256.

Sequence in context: A280177 A241348 A050651 * A279303 A103037 A228309

Adjacent sequences: A233248 A233249 A233250 * A233252 A233253 A233254

Keyword

nonn

Author

R. H. Hardin, Dec 06 2013

Status

approved