A252854 Number of (n+2) X (1+2) 0..2 arrays with every consecutive three elements in every row, column, diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order.

117, 279, 684, 1719, 4383, 11286, 29241, 76059, 198324, 517923, 1353843, 3541014, 9265005, 24247215, 63465660, 166131999, 434901591, 1138526262, 2980601937, 7803157779, 20428674372, 53482546539, 140018449419, 366571967094

Offset

1,1

Links

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

Formula

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

Empirical g.f.: 9*x*(13 - 21*x - 9*x^2 + 6*x^3) / ((1 - 3*x + x^2)*(1 - x - x^2)). - Colin Barker, Dec 07 2018

Example

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

Crossrefs

Column 1 of A252861.

Sequence in context: A304610 A298047 A252861 * A156884 A255022 A217798

Adjacent sequences: A252851 A252852 A252853 * A252855 A252856 A252857

Keyword

nonn

Author

R. H. Hardin, Dec 23 2014

Status

approved