A232370 Number of n X 2 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

2, 14, 58, 230, 934, 3794, 15354, 62266, 252346, 1022806, 4145638, 16802922, 68105158, 276041834, 1118844570, 4534868126, 18380594246, 74499685134, 301959937342, 1223895154962, 4960655920226, 20106384977054, 81494609451994

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 7*a(n-2) + 6*a(n-3) - 2*a(n-4) - 3*a(n-5) + 2*a(n-6) + a(n-7).

Empirical g.f.: 2*x*(1 + 5*x + 8*x^2 + 2*x^3 - 6*x^4 + x^5 + x^6) / ((1 + x)*(1 - 3*x - 4*x^2 - 2*x^3 + 4*x^4 - x^5 - x^6)). - Colin Barker, Oct 05 2018

Example

Some solutions for n=7:
..2..1....0..3....3..2....3..0....3..0....2..3....3..0....1..0....3..2....3..1
..0..3....2..1....1..2....1..2....1..0....0..1....1..0....1..2....1..0....2..1
..0..3....0..1....1..0....3..2....3..2....0..3....1..2....3..2....1..2....2..3
..2..1....2..1....3..0....1..2....1..2....2..3....3..0....3..2....3..2....2..3
..3..1....2..3....2..1....0..3....0..3....0..1....3..2....1..2....3..1....0..1
..0..2....2..1....2..3....0..1....2..1....3..2....1..0....3..0....2..1....0..1
..3..2....0..1....2..3....2..3....3..1....3..2....3..0....1..2....0..3....2..3

Crossrefs

Column 2 of A232376.

Sequence in context: A096367 A232601 A285153 * A174704 A058738 A095376

Adjacent sequences: A232367 A232368 A232369 * A232371 A232372 A232373

Keyword

nonn

Author

R. H. Hardin, Nov 23 2013

Status

approved