A186875 Number of (n+2) X 5 0..3 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

19236, 1201, 6712, 20152, 28984, 32992, 37576, 46624, 73744, 138808, 251563, 430558, 737137, 1213933, 1970809, 3305629, 5489365, 9050326, 15264856, 25456522, 42050491, 70609627, 117651379, 194582923, 326053558, 543547039, 900491803

Offset

1,1

Comments

Column 3 of A186881.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 3*a(n-3) - 6*a(n-4) + 3*a(n-5) + 3*a(n-6) - 3*a(n-7) for n>11.

Empirical g.f.: x*(19236 - 37271*x + 23546*x^2 - 49779*x^3 + 107205*x^4 - 75462*x^5 - 80919*x^6 + 72393*x^7 + 16011*x^8 - 4104*x^9 + 7803*x^10) / ((1 - x)*(1 - x - 3*x^3 + 3*x^4 - 3*x^6)). - Colin Barker, Apr 19 2018

Example

Some solutions for 4 X 5:
..0..0..1..0..0....0..0..0..0..1....0..0..0..1..3....0..0..0..0..0
..1..0..0..1..0....0..0..0..0..0....0..0..0..0..2....0..0..0..0..0
..0..1..0..0..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..1..0..0....2..3..0..0..0....0..0..0..0..0....2..2..0..0..0

Crossrefs

Cf. A186881.

Sequence in context: A210316 A323966 A035925 * A251803 A184667 A280555

Adjacent sequences: A186872 A186873 A186874 * A186876 A186877 A186878

Keyword

nonn

Author

R. H. Hardin, Feb 28 2011

Status

approved