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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 6 04:21 EST 2023. Contains 360097 sequences. (Running on oeis4.)