A197092 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,4,0,0,1 for x=0,1,2,3,4.

1, 7, 18, 55, 163, 484, 1439, 4275, 12704, 37749, 112171, 333314, 990437, 2943067, 8745274, 25986435, 77218255, 229452748, 681814987, 2026001783, 6020230272, 17889013145, 53156902119, 157954841890, 469360159865, 1394695832255

Offset

1,2

Comments

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

Column 2 of A197098.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4).

Empirical g.f.: x*(1 + 5*x + x^2 - 2*x^3) / (1 - 2*x - 3*x^2 + x^4). - Colin Barker, May 11 2018

Example

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

Crossrefs

Cf. A197098.

Sequence in context: A084819 A346494 A220031 * A288743 A223240 A304142

Adjacent sequences: A197089 A197090 A197091 * A197093 A197094 A197095

Keyword

nonn

Author

R. H. Hardin, Oct 10 2011

Status

approved