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

1,8

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

Links

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

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

Example

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

Crossrefs

Column 2 is A297870.

Sequence in context: A298087 A298259 A298930 * A179311 A309983 A342697

Adjacent sequences: A298892 A298893 A298894 * A298896 A298897 A298898

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 28 2018

Status

approved