A253029 Number of (n+2) X (1+2) 0..2 arrays with every consecutive three elements in every row and column having exactly two distinct values, and new values 0 upwards introduced in row major order.

297, 1647, 9126, 50571, 280233, 1552878, 8605089, 47684079, 264235662, 1464230547, 8113859721, 44961990246, 249151530393, 1380643622703, 7650672704694, 42395294391579, 234928490071977, 1301828333534622

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Dec 08 2018: (Start)

G.f.: 27*x*(11 + 6*x) / (1 - 5*x - 3*x^2).

a(n) = (27*2^(-n)*((5-sqrt(37))^n*(-6+sqrt(37)) + (5+sqrt(37))^n*(6+sqrt(37)))) / sqrt(37).

(End)

Example

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

Crossrefs

Column 1 of A253035.

Sequence in context: A179158 A037043 A253035 * A251289 A281132 A200855

Adjacent sequences: A253026 A253027 A253028 * A253030 A253031 A253032

Keyword

nonn

Author

R. H. Hardin, Dec 26 2014

Status

approved