A298087 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 0, 2, 0, 0, 11, 3, 3, 11, 0, 0, 13, 1, 10, 1, 13, 0, 0, 34, 7, 28, 28, 7, 34, 0, 0, 65, 18, 76, 154, 76, 18, 65, 0, 0, 123, 52, 213, 520, 520, 213, 52, 123, 0, 0, 266, 144, 645, 1574, 2767, 1574, 645, 144, 266, 0, 0, 499, 405, 1852, 7204, 11202

Offset: 1

Author

R. H. Hardin, Jan 12 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...0....3.....1......7......18.......52.......144........405........1124

.0...2...3...10....28.....76.....213......645......1852.......5642.......17016

.0..11...1...28...154....520....1574.....7204.....28790.....105055......437163

.0..13...7...76...520...2767...11202....66148....385999....2040394....11280309

.0..34..18..213..1574..11202...65218...479206...3481050...24695892...177272585

.0..65..52..645..7204..66148..479206..4883926..46039875..420410890..3947485108

.0.123.144.1852.28790.385999.3481050.46039875.603770100.7267200831.90210295443

Examples

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

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 16] for n>17

k=4: [order 57] for n>58