A238518 Number of (n+1) X (1+1) 0..3 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors.

84, 588, 7056, 74676, 812028, 8777664, 95006100, 1028017452, 11124397872, 120377861940, 1302620868444, 14095781346528, 152531780288916, 1650560738719116, 17860873095687888, 193274188450247604

Offset

1,1

Links

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

Formula

Empirical: a(n) = 9*a(n-1) + 21*a(n-2) - 14*a(n-3).

Empirical g.f.: 84*x*(1 - 2*x) / (1 - 9*x - 21*x^2 + 14*x^3). - Colin Barker, Oct 24 2018

Example

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

Crossrefs

Column 1 of A238523.

Sequence in context: A008429 A175813 A238523 * A264654 A230907 A220016

Adjacent sequences: A238515 A238516 A238517 * A238519 A238520 A238521

Keyword

nonn

Author

R. H. Hardin, Feb 28 2014

Status

approved