A255021 Number of (n+2) X (2+2) 0..1 arrays with no 3 x 3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 0 or 1 and no column sum 0 or 1.

54, 134, 405, 1121, 3015, 8338, 23077, 63446, 174690, 481563, 1326665, 3654411, 10068170, 27738103, 76416448, 210524442, 579990071, 1597852613, 4402027923, 12127445276, 33410714325, 92045405668, 253582052728, 698610194507

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(54 + 80*x + 163*x^2 + 124*x^3 + 10*x^4 - 73*x^5 - 68*x^6 - 31*x^7 - 2*x^8) / (1 - x - 2*x^2 - 6*x^3 - 5*x^4 - x^5 + 2*x^6 + 2*x^7 + x^8). - Colin Barker, Dec 18 2018

Example

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

Crossrefs

Column 2 of A255027.

Sequence in context: A043446 A044241 A044622 * A184067 A044305 A044686

Adjacent sequences: A255018 A255019 A255020 * A255022 A255023 A255024

Keyword

nonn

Author

R. H. Hardin, Feb 13 2015

Status

approved