A298070 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 6 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, 253, 346, 346, 253, 54, 0, 0, 125, 953, 2197, 3500, 2197, 953, 125, 0, 0, 282, 3802, 13350, 33869, 33869, 13350, 3802, 282, 0, 0, 641, 15108, 84657, 302143, 532282

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........253..........953..........3802

.0...5....13.....59......346.......2197........13350.........84657

.0..10....63....346.....3500......33869.......302143.......2864336

.0..25...253...2197....33869.....532282......7794251.....117272307

.0..54...953..13350...302143....7794251....180902016....4321153141

.0.125..3802..84657..2864336..117272307...4321153141..162145163369

.0.282.15108.529728.26751944.1752542571.102552409457.6062432627760

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 17]

k=4: [order 62] for n>63

Example

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

Crossrefs

Column 2 is A297860.

Sequence in context: A370374 A297866 A298133 * A298719 A296148 A121178

Adjacent sequences: A298067 A298068 A298069 * A298071 A298072 A298073

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 11 2018

Status

approved