A304894 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 11, 24, 1, 1, 82, 40, 40, 82, 1, 1, 272, 94, 246, 94, 272, 1, 1, 908, 291, 899, 899, 291, 908, 1, 1, 3076, 776, 4262, 3145, 4262, 776, 3076, 1, 1, 10444, 2269, 18773, 17391, 17391, 18773, 2269, 10444, 1, 1, 35480, 6275, 86217

Offset

1,5

Comments

Table starts

.1.....1....1......1.......1........1.........1..........1............1

.1.....4....8.....24......82......272.......908.......3076........10444

.1.....8...11.....40......94......291.......776.......2269.........6275

.1....24...40....246.....899.....4262.....18773......86217.......393045

.1....82...94....899....3145....17391.....86300.....437461......2277571

.1...272..291...4262...17391...123297....793698....5028590.....34392736

.1...908..776..18773...86300...793698...7309444...56105221....545744025

.1..3076.2269..86217..437461..5028590..56105221..527157688...6329865862

.1.10444.6275.393045.2277571.34392736.545744025.6329865862.106200560327

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

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

k=4: [order 49] for n>52

Example

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

Crossrefs

Column 2 is A303882.

Sequence in context: A174035 A303888 A305281 * A316576 A304551 A316376

Adjacent sequences: A304891 A304892 A304893 * A304895 A304896 A304897

Keyword

nonn,tabl

Author

R. H. Hardin, May 20 2018

Status

approved