A194540 T(n,k) is the number of lower triangles of an n X n 0..k array with new values introduced in row major order 0..k and no element equal to more than one horizontal or vertical neighbor.

1, 1, 3, 1, 4, 6, 1, 4, 59, 12, 1, 4, 116, 1851, 23, 1, 4, 131, 16556, 119548, 43, 1, 4, 132, 43785, 7721920, 16039294, 79, 1, 4, 132, 62038, 79201795, 11525456507, 4460214471, 143, 1, 4, 132, 67377, 286773762, 627974590650, 54979732214116, 2572187445993

Offset: 1

Author

R. H. Hardin, Aug 28 2011

Keywords

• nonn
• tabl

Examples

			Table starts:
...1.............1..................1......................1
...3.............4..................4......................4
...6............59................116....................131
..12..........1851..............16556..................43785
..23........119548............7721920...............79201795
..43......16039294........11525456507...........627974590650
..79....4460214471.....54979732214116......21399815343394998
.143.2572187445993.838387866908847478.3132305932642809585983
Some solutions for n=4 and k=3:
..0........0........0........0........0........0........0........0
..1.2......1.0......1.0......1.0......0.1......1.2......1.0......1.2
..3.1.1....0.1.0....2.0.3....2.3.1....2.3.0....1.3.3....2.3.3....0.3.1
..2.3.2.0..2.1.3.1..2.1.0.1..1.0.3.2..3.0.3.1..3.1.1.2..0.2.2.0..2.1.2.1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..86

Crossrefs

Column 1 is A055244.