A252856 Number of (n+2) X (3+2) 0..2 arrays with every consecutive three elements in every row, column, diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order.

684, 738, 1197, 1962, 3582, 6795, 12762, 24552, 47367, 91440, 176940, 342711, 663624, 1285704, 2490993, 4826304, 9351324, 18119295, 35108028, 68026230, 131809365, 255397428, 494865270, 958865463, 1857925458, 3599971020

Offset

1,1

Links

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

Formula

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

Empirical g.f.: 9*x*(76 - 70*x - 31*x^2 - 48*x^3 - 38*x^4 + 35*x^5 - 86*x^6 + 95*x^7 - 20*x^8 - 2*x^9) / ((1 - x)*(1 + x + x^2)*(1 - 2*x + x^3 - 2*x^4 + x^5)). - Colin Barker, Dec 07 2018

Example

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

Crossrefs

Column 3 of A252861.

Sequence in context: A344202 A015386 A245393 * A184089 A254071 A022050

Adjacent sequences: A252853 A252854 A252855 * A252857 A252858 A252859

Keyword

nonn

Author

R. H. Hardin, Dec 23 2014

Status

approved