A252723 Number of (4+2) X (n+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.

84, 76, 80, 97, 112, 132, 153, 196, 224, 277, 352, 420, 513, 676, 800, 997, 1312, 1572, 1953, 2596, 3104, 3877, 5152, 6180, 7713, 10276, 12320, 15397, 20512, 24612, 30753, 40996, 49184, 61477, 81952, 98340, 122913, 163876, 196640, 245797, 327712, 393252

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) - 2*a(n-6) - 2*a(n-7) for n>8.

Empirical g.f.: x*(84 + 160*x + 156*x^2 - 75*x^3 - 271*x^4 - 224*x^5 - 78*x^6 + 42*x^7) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 - 2*x^3)). - Colin Barker, Dec 06 2018

Example

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

Crossrefs

Row 4 of A252719.

Sequence in context: A066689 A008898 A033404 * A341304 A128873 A095607

Adjacent sequences: A252720 A252721 A252722 * A252724 A252725 A252726

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved