A186565 Number of (n+2) X 8 0..2 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

20056, 3379, 5605, 12895, 23389, 29935, 36133, 44887, 60493, 91519, 137701, 205879, 317293, 498159, 754229, 1158823, 1794685, 2717311, 4159813, 6426583, 9779021, 14980399, 23102037, 35240263, 53961373, 83056543, 126889765, 194291511

Offset

1,1

Comments

Column 6 of A186568.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) + 2*a(n-6) - 2*a(n-7) for n>14.

Empirical g.f.: x*(20056 - 36733*x + 18903*x^2 - 35048*x^3 + 76670*x^4 - 41754*x^5 - 50588*x^6 + 29502*x^7 + 10296*x^8 + 1536*x^9 - 10944*x^10 - 4800*x^11 + 21632*x^13) / ((1 - x)*(1 - x - 2*x^3 + 2*x^4 - 2*x^6)). - Colin Barker, Apr 18 2018

Example

Some solutions for 4 X 8:
..1..0..0..0..0..0..0..1....2..0..0..0..0..0..1..0....0..0..0..0..2..0..0..1
..0..1..0..0..0..0..0..0....0..2..0..0..0..0..0..0....0..0..0..0..0..2..0..0
..0..0..1..0..0..0..0..0....0..0..2..0..0..0..0..0....1..0..0..0..0..0..2..0
..2..0..0..1..0..0..0..0....1..0..0..2..0..0..0..2....0..2..0..0..0..0..0..2

Crossrefs

Cf. A186568.

Sequence in context: A236115 A251986 A251880 * A186480 A204864 A353034

Adjacent sequences: A186562 A186563 A186564 * A186566 A186567 A186568

Keyword

nonn

Author

R. H. Hardin, Feb 23 2011

Status

approved