A252714 Number of (n+2) X (3+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.

70, 50, 62, 80, 119, 170, 224, 341, 494, 656, 1007, 1466, 1952, 3005, 4382, 5840, 8999, 13130, 17504, 26981, 39374, 52496, 80927, 118106, 157472, 242765, 354302, 472400, 728279, 1062890, 1417184, 2184821, 3188654, 4251536, 6554447, 9565946, 12754592

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) for n>6.

Empirical g.f.: x*(70 - 20*x + 12*x^2 - 192*x^3 + 99*x^4 + 15*x^5) / ((1 - x)*(1 - 3*x^3)). - Colin Barker, Dec 05 2018

Example

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

Crossrefs

Column 3 of A252719.

Sequence in context: A129352 A318571 A156810 * A245046 A265727 A166506

Adjacent sequences: A252711 A252712 A252713 * A252715 A252716 A252717

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved