A252690 Number of (n+2) X (3+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.

148, 204, 134, 407, 291, 881, 727, 2067, 2067, 5331, 6491, 15287, 22035, 48395, 79207, 166155, 295755, 604671, 1132307, 2284763, 4405335, 8834267, 17313499, 34630815, 68480739, 136855275, 271964087, 543415691, 1082854443, 2163899807, 4318574515

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 7*a(n-3) + 2*a(n-4) + 6*a(n-5) + 14*a(n-6) - 20*a(n-7) - 4*a(n-8) + 8*a(n-9) for n>10.

Empirical g.f.: x*(148 - 388*x - 386*x^2 + 1315*x^3 + 63*x^4 + 173*x^5 - 2930*x^6 + 1444*x^7 + 1192*x^8 - 608*x^9) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 2*x^3)). - Colin Barker, Dec 05 2018

Example

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

Crossrefs

Column 3 of A252695.

Sequence in context: A308889 A214619 A061154 * A134212 A344409 A127028

Adjacent sequences: A252687 A252688 A252689 * A252691 A252692 A252693

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved