A267724 T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to at least one horizontal neighbor and the top left element equal to 0.

0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 3, 2, 6, 0, 1, 5, 30, 6, 24, 0, 1, 12, 58, 630, 24, 120, 0, 1, 26, 588, 1398, 22680, 120, 720, 0, 1, 60, 2388, 93672, 55896, 1247400, 720, 5040, 0, 1, 143, 17456, 609264, 33807456, 3353880, 97297200, 5040, 40320, 0, 1, 353, 102874

Offset: 1

Author

R. H. Hardin, Jan 20 2016

Keywords

• nonn
• tabl

Comments

Table starts

.0......1.....1...........1.........1...........1.........1........1.........1

.0......1.....1...........3.........5..........12........26.......60.......143

.0......2.....2..........30........58.........588......2388....17456....102874

.0......6.....6.........630......1398.......93672....609264.20702760.279681294

.0.....24....24.......22680.....55896....33807456.331295040

.0....120...120.....1247400...3353880.22933860480

.0....720...720....97297200.281725200

.0...5040..5040.10216206000

.0..40320.40320

.0.362880

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..70

Crossrefs

Column 2 and column 3 are A000142(n-1).

Column 4 is A007019(n-1).