A252712 Number of (n+2) X (1+2) 0..3 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

39, 45, 54, 84, 111, 165, 257, 376, 560, 930, 1365, 2091, 3503, 5206, 8006, 13536, 20163, 31137, 52829, 78868, 122012, 207582, 310257, 480663, 819275, 1225618, 1900658, 3244188, 4856415, 7536909, 12878201, 19287760, 29950664, 51217434

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 6*a(n-3) - 7*a(n-4) - 7*a(n-5) - 5*a(n-6) + 12*a(n-7) + 12*a(n-8) - 12*a(n-9) for n>11.

Empirical g.f.: x*(39 + 6*x - 30*x^2 - 249*x^3 - 24*x^4 + 234*x^5 + 365*x^6 + 11*x^7 - 436*x^8 + 84*x^9 + 12*x^10) / ((1 - x)^2*(1 + x)*(1 - 3*x^3)*(1 - 4*x^3)). - Colin Barker, Dec 05 2018

Example

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

Crossrefs

Column 1 of A252719.

Sequence in context: A061756 A236673 A119028 * A252711 A046512 A143746

Adjacent sequences: A252709 A252710 A252711 * A252713 A252714 A252715

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved