A316123 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 23, 23, 26, 1, 1, 49, 47, 56, 47, 49, 1, 1, 99, 144, 213, 213, 144, 99, 1, 1, 194, 391, 702, 1109, 702, 391, 194, 1, 1, 387, 1118, 2524, 5426, 5426, 2524, 1118, 387, 1, 1, 773, 3330, 9034, 26626, 43480, 26626, 9034

Offset

1,5

Comments

Table starts

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

.1...4....7....13.....26.......49........99........194..........387

.1...7...13....23.....47......144.......391.......1118.........3330

.1..13...23....56....213......702......2524.......9034........33185

.1..26...47...213...1109.....5426.....26626.....133245.......708063

.1..49..144...702...5426....43480....283238....2064800.....15977233

.1..99..391..2524..26626...283238...2525039...25192165....261795432

.1.194.1118..9034.133245..2064800..25192165..351431316...5223691497

.1.387.3330.33185.708063.15977233.261795432.5223691497.112149224917

Links

R. H. Hardin, Table of n, a(n) for n = 1..197

Formula

Empirical for column k:

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

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

k=3: [order 17] for n>19

k=4: [order 70] for n>71

Example

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

Crossrefs

Column 2 is A304004.

Sequence in context: A304952 A316620 A304676 * A146771 A073697 A209414

Adjacent sequences: A316120 A316121 A316122 * A316124 A316125 A316126

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 24 2018

Status

approved