A298719 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 5, 4, 5, 0, 0, 10, 13, 13, 10, 0, 0, 25, 63, 59, 63, 25, 0, 0, 54, 264, 346, 346, 264, 54, 0, 0, 125, 1005, 2246, 3508, 2246, 1005, 125, 0, 0, 282, 4113, 13650, 34704, 34704, 13650, 4113, 282, 0, 0, 641, 16720, 87117, 309593, 563977

Offset

1,8

Comments

Table starts

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

.0...1.....2......5.......10.........25...........54...........125

.0...2.....4.....13.......63........264.........1005..........4113

.0...5....13.....59......346.......2246........13650.........87117

.0..10....63....346.....3508......34704.......309593.......2960634

.0..25...264...2246....34704.....563977......8287084.....125919136

.0..54..1005..13650...309593....8287084....193439202....4672566734

.0.125..4113..87117..2960634..125919136...4672566734..177476979652

.0.282.16720.550582.27934888.1909040369.112689610775.6748480839625

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) = 3*a(n-2) +4*a(n-3) +2*a(n-4)

k=3: [order 18]

k=4: [order 63] for n>64

Example

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

Crossrefs

Column 2 is A297860.

Sequence in context: A297866 A298133 A298070 * A296148 A121178 A175917

Adjacent sequences: A298716 A298717 A298718 * A298720 A298721 A298722

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 25 2018

Status

approved