A298895 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 1, 2, 0, 0, 11, 4, 4, 11, 0, 0, 13, 4, 11, 4, 13, 0, 0, 34, 11, 31, 31, 11, 34, 0, 0, 65, 26, 80, 219, 80, 26, 65, 0, 0, 123, 66, 229, 579, 579, 229, 66, 123, 0, 0, 266, 171, 681, 1858, 2963, 1858, 681, 171, 266, 0, 0, 499, 462, 1969, 8891, 12224

Offset: 1

Author

R. H. Hardin, Jan 28 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0...0...0....0.....0......0.......0........0.........0..........0............0

.0...1...3....2....11.....13......34.......65.......123........266..........499

.0...3...1....4.....4.....11......26.......66.......171........462.........1248

.0...2...4...11....31.....80.....229......681......1969.......5973........18031

.0..11...4...31...219....579....1858.....8891.....34212.....128103.......538967

.0..13..11...80...579...2963...12224....72620....426475....2284203.....12768382

.0..34..26..229..1858..12224...74725...547497...4012035...28805843....209118279

.0..65..66..681..8891..72620..547497..5719782..54423404..502721390...4804572705

.0.123.171.1969.34212.426475.4012035.54423404.724538480.8857192378.112203393143

Examples

			Some solutions for n=7 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..0..0..1. .1..0..0..1
..0..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..0..1. .0..1..1..0
..0..0..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1. .0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..219

Crossrefs

Column 2 is A297870.

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)

k=3: [order 17] for n>18

k=4: [order 58] for n>59