A186460 Number of (n+1) X 8 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

245, 292, 590, 945, 1681, 2377, 4121, 5633, 8893, 11977, 19037, 27133, 43249, 63485, 98801, 146333, 225061, 336241, 513933, 771609, 1174525, 1768605, 2685617, 4051469, 6143169, 9277789, 14055269, 21241521, 32162333, 48626537, 73602781

Offset

1,1

Comments

Column 7 of A186462.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>13.

Empirical g.f.: x*(245 - 198*x + 6*x^2 + 255*x^3 - 115*x^4 - 144*x^5 + 369*x^6 - 547*x^7 - 36*x^8 - 640*x^9 + 484*x^10 - 300*x^11 + 784*x^12) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 18 2018

Example

Some solutions for 3 X 8:
..0..1..0..0..0..0..0..1....1..0..0..0..1..0..1..0....1..0..0..0..0..0..0..0
..1..0..1..0..0..0..0..0....1..0..0..0..0..1..0..1....1..0..0..0..0..0..0..0
..0..1..0..1..0..0..0..0....1..0..0..0..0..0..1..0....1..0..0..0..0..0..0..0

Crossrefs

Cf. A186462.

Sequence in context: A233821 A216233 A157246 * A171994 A129210 A137521

Adjacent sequences: A186457 A186458 A186459 * A186461 A186462 A186463

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved