A190025 Number of (n+2) X 3 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

512, 112, 228, 415, 616, 880, 1205, 1508, 2008, 2793, 3776, 5220, 7274, 9829, 13345, 18256, 24651, 33451, 45700, 61988, 84197, 114766, 155769, 211493, 287826, 390881, 530866, 722029, 980917, 1332459, 1811512, 2461345, 3343817, 4544963, 6175777

Offset

1,1

Comments

Column 1 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>11.

Empirical g.f.: x*(512 - 912*x + 516*x^2 - 441*x^3 + 926*x^4 - 453*x^5 - 522*x^6 + 364*x^7 + 18*x^8 + 37*x^9 + 19*x^10) / ((1 - x)*(1 - x - x^3 + x^4 - x^6)). - Colin Barker, May 03 2018

Example

Some solutions for 4 X 3:
..1..1..0....1..1..0....0..0..0....0..0..0....1..1..1....1..1..1....1..0..0
..1..1..0....0..1..1....0..0..0....0..0..0....0..0..0....0..1..1....0..1..0
..1..1..0....0..1..0....0..0..0....1..1..0....0..0..0....0..0..0....0..1..0
..0..1..1....0..0..1....1..1..0....0..0..1....0..0..0....0..0..0....0..1..0

Crossrefs

Cf. A190033.

Sequence in context: A190024 A376951 A190033 * A077743 A111447 A224563

Adjacent sequences: A190022 A190023 A190024 * A190026 A190027 A190028

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved