A196631 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,0,4 for x=0,1,2,3,4.

1, 5, 21, 62, 232, 780, 2716, 9427, 32612, 113008, 391387, 1355818, 4696609, 16268643, 56353996, 195208062, 676193929, 2342310759, 8113674993, 28105465903, 97356282867, 337238520190, 1168181597226, 4046537274472, 14017053521933

Offset

1,2

Comments

Every 0 is next to 0 1's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 4's.

Column 3 of A196636.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 4*a(n-3) + 5*a(n-4) + 5*a(n-5) - 12*a(n-6) - a(n-8) - 4*a(n-9) for n>10.

Empirical g.f.: x*(1 + 2*x + 6*x^2 - 5*x^3 + 21*x^4 - 30*x^5 + 10*x^6 - 4*x^7 - 6*x^8 + x^9) / (1 - 3*x - 4*x^3 - 5*x^4 - 5*x^5 + 12*x^6 + x^8 + 4*x^9). - Colin Barker, Mar 01 2018

Example

Some solutions for n=4:
..0..0..0....0..0..0....0..0..0....0..0..0....0..3..0....0..3..0....0..0..0
..0..0..3....0..2..2....0..0..3....3..0..0....0..0..0....0..0..3....0..0..0
..0..0..0....0..2..2....3..0..0....0..2..2....0..0..3....3..0..0....3..0..3
..0..3..0....0..0..0....0..0..0....0..2..2....0..3..0....0..0..0....0..0..0

Crossrefs

Cf. A196636.

Sequence in context: A356328 A147216 A362573 * A357723 A342379 A146822

Adjacent sequences: A196628 A196629 A196630 * A196632 A196633 A196634

Keyword

nonn

Author

R. H. Hardin, Oct 04 2011

Status

approved