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

1,1

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.

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

Example

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

Crossrefs

Sequence in context: A222856 A342583 A007990 * A354387 A121188 A331678

Adjacent sequences: A197047 A197048 A197049 * A197051 A197052 A197053

Keyword

nonn

Author

R. H. Hardin, Oct 09 2011

Status

approved