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

1,5

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297852.

Column 3 is A298050.

Column 4 is A298656.

Sequence in context: A298055 A298888 A298660 * A297959 A298775 A298582

Adjacent sequences: A299609 A299610 A299611 * A299613 A299614 A299615

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 14 2018

Status

approved