A241125 Number of n X 2 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

2, 9, 54, 325, 1965, 11876, 71793, 434007, 2623694, 15861001, 95884409, 579649484, 3504151829, 21183629803, 128061281038, 774168159805, 4680074530261, 28292428888436, 171036065180937, 1033963386740399, 6250613190784174

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + 2*a(n-2) - 9*a(n-3) - 10*a(n-4) + 8*a(n-5) for n>6.

Empirical g.f.: x*(1 - x)*(1 - 2*x)*(2 + 3*x + x^2 - 2*x^3) / (1 - 6*x - 2*x^2 + 9*x^3 + 10*x^4 - 8*x^5). - Colin Barker, Oct 29 2018

Example

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

Crossrefs

Column 2 of A241130.

Sequence in context: A073986 A223943 A371698 * A370474 A089436 A368178

Adjacent sequences: A241122 A241123 A241124 * A241126 A241127 A241128

Keyword

nonn

Author

R. H. Hardin, Apr 16 2014

Status

approved