A190026 Number of (n+2) X 4 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

112, 45, 79, 155, 235, 295, 355, 423, 531, 740, 1037, 1434, 1992, 2706, 3628, 4920, 6665, 9015, 12293, 16738, 22710, 30902, 42006, 56987, 77466, 105302, 142987, 194362, 264198, 358864, 487699, 662831, 900478, 1223669, 1662993, 2259498

Offset

1,1

Comments

Column 2 of A190033.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

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

Empirical g.f.: x*(112 - 179*x + 101*x^2 - 70*x^3 + 183*x^4 - 121*x^5 - 154*x^6 + 71*x^7 + 26*x^8 + 25*x^9) / ((1 - x)*(1 - x - x^3 + x^4 - x^6)). - Colin Barker, May 03 2018

Example

Some solutions for 6 X 4:
..0..0..1..1....0..0..0..0....0..0..0..0....1..1..0..1....0..0..0..0
..0..0..0..1....0..0..0..0....0..0..0..0....0..1..1..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....1..0..1..1....0..0..0..0
..0..0..0..0....1..0..0..0....0..0..0..0....1..1..0..1....0..0..0..0
..0..0..0..0....1..1..0..0....1..0..0..0....0..1..1..0....1..0..0..0
..1..1..1..1....1..1..1..0....0..0..0..1....1..0..1..1....0..1..0..0

Crossrefs

Cf. A190033.

Sequence in context: A103849 A340470 A010032 * A129947 A217148 A223822

Adjacent sequences: A190023 A190024 A190025 * A190027 A190028 A190029

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved