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

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)