A233021 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

9, 81, 849, 8835, 92067, 959385, 9997413, 104179551, 1085618895, 11312857317, 117887355777, 1228463178219, 12801387988827, 133398816787089, 1390102724464989, 14485777543658775, 150951255149241255

Offset

1,1

Links

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

Formula

Empirical: a(n) = 11*a(n-1) - 5*a(n-2) - 11*a(n-3) + 2*a(n-4).

Empirical g.f.: 3*x*(3 - 6*x + x^2) / (1 - 11*x + 5*x^2 + 11*x^3 - 2*x^4). - Colin Barker, Oct 07 2018

Example

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

Crossrefs

Column 3 of A233026.

Sequence in context: A001514 A077364 A077486 * A366273 A187122 A113361

Adjacent sequences: A233018 A233019 A233020 * A233022 A233023 A233024

Keyword

nonn

Author

R. H. Hardin, Dec 03 2013

Status

approved