A317222 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 133, 98, 3, 5, 383, 929, 929, 383, 5, 8, 1493, 6134, 11378, 6134, 1493, 8, 13, 5824, 40873, 133874, 133874, 40873, 5824, 13, 21, 22717, 272012, 1580822, 2762836, 1580822, 272012, 22717, 21, 34, 88609, 1810626

Offset

1,5

Comments

Table starts

..0.....1........1..........2............3...............5.................8

..1.....7.......25.........98..........383............1493..............5824

..1....25......133........929.........6134...........40873............272012

..2....98......929......11378.......133874.........1580822..........18667993

..3...383.....6134.....133874......2762836........57448875........1193567097

..5..1493....40873....1580822.....57448875......2106680104.......77171164500

..8..5824...272012...18667993...1193567097.....77171164500.....4981964443017

.13.22717..1810626..220464927..24804953660...2827889481366...321779228843527

.21.88609.12051365.2603595850.515450451064.103616727948480.20780911115253208

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) +a(n-2)

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

k=3: [order 9] for n>10

k=4: [order 28] for n>29

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304421.

Sequence in context: A304427 A316282 A305961 * A305692 A317072 A316953

Adjacent sequences: A317219 A317220 A317221 * A317223 A317224 A317225

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 23 2018

Status

approved