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

1,3

Links

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

Example

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

Crossrefs

Column 1 is A055244.

Sequence in context: A243553 A286159 A307394 * A351153 A193043 A086271

Adjacent sequences: A194537 A194538 A194539 * A194541 A194542 A194543

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 28 2011

Status

approved