A197050 Number of nX4 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.

3, 6, 18, 42, 108, 274, 692, 1754, 4442, 11248, 28488, 72146, 182712, 462728, 1171876, 2967826, 7516146, 19034954, 48206826, 122085820, 309187486, 783030352, 1983057390, 5022176478, 12718873752, 32211084212, 81575929322, 206594481604

Offset: 1

Author

R. H. Hardin, Oct 09 2011

Keywords

• nonn

Comments

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

Column 4 of A197054.

Examples

			Some solutions for n=5
..0..2..1..0....2..0..3..0....0..3..0..2....2..0..3..0....0..3..0..1
..3..0..2..1....0..4..0..3....3..0..4..0....0..4..0..3....2..0..2..1
..0..4..0..2....2..0..4..0....0..4..0..2....3..0..3..0....1..1..2..0
..3..0..4..0....1..2..0..3....3..0..2..1....0..2..1..1....0..3..0..3
..0..3..0..2....0..1..2..0....0..2..1..0....1..1..0..1....2..0..3..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

Equivalent empirical g.f.: 3*x - 2*x^2*(1+x)*(x^4+3*x^3-3*x-3) / ( 1-x-3*x^2-3*x^3+x^4+2*x^5+x^6 ). - R. J. Mathar, Oct 10 2011