A298461 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 6, 8, 6, 0, 0, 17, 30, 30, 17, 0, 0, 41, 153, 219, 153, 41, 0, 0, 104, 710, 2013, 2013, 710, 104, 0, 0, 261, 3490, 17443, 35980, 17443, 3490, 261, 0, 0, 655, 17087, 158594, 603930, 603930, 158594, 17087, 655, 0, 0, 1646, 84008, 1441287

Offset

1,8

Comments

Table starts

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

.0...1.....3........6.........17...........41.............104...............261

.0...3.....8.......30........153..........710............3490.............17087

.0...6....30......219.......2013........17443..........158594...........1441287

.0..17...153.....2013......35980.......603930........10408388.........179761398

.0..41...710....17443.....603930.....19100497.......628485305.......20637616811

.0.104..3490...158594...10408388....628485305.....39291988976.....2452094749578

.0.261.17087..1441287..179761398..20637616811...2452094749578...290849365371077

.0.655.84008.13145287.3109300283.679019933720.153330900615477.34561341191060912

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 13] for n>15

k=4: [order 37] for n>38

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
..0..1..0..1. .1..0..0..1. .0..0..0..1. .0..0..1..1. .1..0..0..0
..1..1..1..0. .1..1..1..1. .1..0..1..1. .0..1..1..1. .1..1..1..1
..0..0..0..0. .1..1..0..1. .1..1..0..0. .1..0..0..0. .1..0..0..1
..0..0..0..0. .1..1..0..0. .1..1..0..0. .1..1..0..0. .0..0..1..1

Crossrefs

Column 2 is A297972.

Sequence in context: A335681 A297978 A298629 * A299334 A268759 A298841

Adjacent sequences: A298458 A298459 A298460 * A298462 A298463 A298464

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 19 2018

Status

approved