A186874 Number of (n+2) X 4 0..3 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

2428, 421, 1201, 6829, 14221, 18517, 21661, 25381, 34645, 64384, 118027, 201190, 355210, 592102, 945346, 1600378, 2664955, 4328077, 7358623, 12328480, 20153704, 34046296, 56950552, 93410275, 157163740, 262861768, 432701869, 726100972

Offset

1,1

Comments

Column 2 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>10.

Empirical g.f.: x*(2428 - 4435*x + 2787*x^2 - 2436*x^3 + 15069*x^4 - 11457*x^5 - 22980*x^6 + 1305*x^7 + 12492*x^8 + 7047*x^9) / ((1 - x)*(1 - x - 3*x^3 + 3*x^4 - 3*x^6)). - Colin Barker, Apr 19 2018

Example

Some solutions for 6 X 4:
..0..0..2..0....1..0..0..0....0..0..3..0....1..0..0..0....1..1..1..1
..0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..3....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..3..0..0..0....3..0..0..0....2..0..0..0....0..0..0..0....3..0..0..0
..2..3..0..0....0..2..0..0....2..2..0..0....0..0..0..3....3..1..0..0

Crossrefs

Cf. A186881.

Sequence in context: A078868 A340433 A340899 * A345174 A345175 A202201

Adjacent sequences: A186871 A186872 A186873 * A186875 A186876 A186877

Keyword

nonn

Author

R. H. Hardin, Feb 28 2011

Status

approved