A188101 Number of (n+3) X 8 binary arrays with every 4 X 4 subblock commuting with each horizontal and vertical neighbor 4 X 4 subblock.

8274, 1482, 3013, 5037, 7661, 8509, 8873, 9265, 9825, 10805, 13085, 16429, 22789, 30417, 41390, 53819, 69824, 88077, 111955, 140633, 179247, 227737, 292825, 375142, 483400, 619787, 796650, 1019420, 1306745, 1670689, 2140197, 2737929, 3508474

Offset

1,1

Comments

Column 5 of A188105.

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-4) - 2*a(n-5) + a(n-6) + a(n-8) - a(n-9) for n>15.

Empirical g.f.: x*(8274 - 15066*x + 8323*x^2 + 493*x^3 - 7674*x^4 + 13290*x^5 - 8807*x^6 - 465*x^7 - 8706*x^8 + 8988*x^9 + 253*x^10 - 988*x^11 + 224*x^12 + 1681*x^14) / ((1 - x)*(1 - x - x^4 + x^5 - x^8)). - Colin Barker, Feb 15 2018

Example

Some solutions for 5 X 8:
..0..0..0..0..0..1..0..0....1..1..0..0..1..1..0..0....0..0..0..0..0..0..1..0
..0..0..0..0..0..0..0..0....0..1..1..0..0..1..1..0....0..0..0..0..0..0..0..1
..0..0..0..0..0..0..0..0....0..0..1..1..0..0..1..1....1..0..0..0..0..0..0..0
..1..0..0..0..0..0..0..0....1..0..0..1..1..0..0..1....1..0..0..0..0..0..0..0
..0..0..0..0..0..0..0..0....1..1..0..0..1..1..0..0....0..1..0..0..0..0..0..0

Crossrefs

Sequence in context: A345851 A166194 A269959 * A157731 A252581 A271748

Adjacent sequences: A188098 A188099 A188100 * A188102 A188103 A188104

Keyword

nonn

Author

R. H. Hardin, Mar 20 2011

Status

approved