A299588 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 16, 1, 16, 0, 1, 48, 8, 8, 48, 1, 0, 88, 12, 84, 12, 88, 0, 1, 240, 31, 229, 229, 31, 240, 1, 0, 704, 117, 720, 2170, 720, 117, 704, 0, 1, 1600, 263, 4326, 6418, 6418, 4326, 263, 1600, 1, 0, 4032, 689, 15638, 58139, 38420, 58139, 15638, 689

Offset

1,5

Comments

Table starts

.0....1...0.....1.......0........1..........0............1.............0

.1....4...4....16......48.......88........240..........704..........1600

.0....4...1.....8......12.......31........117..........263...........689

.1...16...8....84.....229......720.......4326........15638.........62867

.0...48..12...229....2170.....6418......58139.......462269.......2322276

.1...88..31...720....6418....38420.....551191......5070055......45637326

.0..240.117..4326...58139...551191...12345692....187346100....2776620332

.1..704.263.15638..462269..5070055..187346100...5383097328..108788947080

.0.1600.689.62867.2322276.45637326.2776620332.108788947080.3979108348246

Links

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

Formula

Empirical for column k:

k=1: a(n) = a(n-2)

k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)

k=3: [order 19] for n>20

k=4: [order 64] for n>65

Example

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

Crossrefs

Column 2 is A298448.

Sequence in context: A298622 A298454 A298834 * A299528 A300146 A100045

Adjacent sequences: A299585 A299586 A299587 * A299589 A299590 A299591

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 13 2018

Status

approved