A299612 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 85, 85, 34, 95, 13, 21, 177, 63, 173, 179, 173, 63, 177, 21, 34, 359, 96, 322, 453, 453, 322, 96, 359, 34, 55, 705, 147, 635, 1006, 1223, 1006, 635, 147, 705, 55, 89, 1351

Offset: 1

Author

R. H. Hardin, Feb 14 2018

Keywords

• nonn
• tabl

Comments

Table starts

..0...1...1....2....3.....5......8......13......21.......34........55

..1...3...7...13...23....49.....95.....177.....359......705......1351

..1...7..15...19...23....34.....63......96.....147......233.......368

..2..13..19...40...85...173....322.....635....1325.....2806......5877

..3..23..23...85..179...453...1006....2523....6002....14802.....36299

..5..49..34..173..453..1223...3286....9873...28227....86428....253623

..8..95..63..322.1006..3286..13490...49047..183585...713699...2714170

.13.177..96..635.2523..9873..49047..231838.1084038..5339757..25938953

.21.359.147.1325.6002.28227.183585.1084038.6506278.41165944.255972254

Examples

			Some solutions for n=6 k=6
..0..1..1..1..0..1. .0..1..1..0..0..0. .0..1..0..1..0..0. .0..1..0..1..1..0
..0..0..1..1..1..0. .0..0..0..0..0..1. .0..1..0..1..0..1. .0..1..0..0..0..0
..1..1..1..1..1..1. .0..0..0..0..1..0. .1..1..1..1..1..1. .0..1..0..0..0..0
..0..0..1..1..1..1. .1..0..0..0..0..1. .0..0..1..1..1..1. .1..0..0..0..0..1
..1..1..1..0..0..1. .0..1..0..1..0..1. .1..1..1..1..1..0. .1..0..1..0..0..1
..0..0..1..0..1..1. .0..1..0..1..0..0. .0..0..1..1..0..1. .0..1..0..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297852.

Column 3 is A298050.

Column 4 is A298656.

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6

k=3: [order 18] for n>19

k=4: [order 72] for n>73