A252689 Number of (n+2) X (2+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and in every diagonal and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

96, 142, 204, 519, 1047, 2719, 6483, 16887, 42825, 111655, 288975, 754413, 1965903, 5137567, 13421949, 35100447, 91797087, 240169717, 628416399, 1644575439, 4304194509, 11265951439, 29489332431, 77193738645, 202074840159

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 4*a(n-2) - 11*a(n-3) + 9*a(n-4) + 12*a(n-5) + 12*a(n-6) - 34*a(n-7) - 8*a(n-8) + 28*a(n-9) - 8*a(n-10) for n>11.

Empirical g.f.: x*(96 - 338*x - 122*x^2 + 1123*x^3 - 34*x^4 - 626*x^5 - 1907*x^6 + 1306*x^7+ 1728*x^8 - 1488*x^9 + 288*x^10) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x + x^2)*(1 - 2*x^2)*(1 - 2*x^3)). - Colin Barker, Dec 05 2018

Example

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

Crossrefs

Column 2 of A252695.

Sequence in context: A323629 A146992 A261287 * A253392 A116119 A039600

Adjacent sequences: A252686 A252687 A252688 * A252690 A252691 A252692

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved