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A305089 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 7, 1, 2, 14, 14, 2, 3, 33, 22, 33, 3, 5, 70, 34, 34, 70, 5, 8, 157, 182, 91, 182, 157, 8, 13, 346, 438, 352, 352, 438, 346, 13, 21, 769, 920, 372, 3384, 372, 920, 769, 21, 34, 1710, 3431, 1016, 15814, 15814, 1016, 3431, 1710, 34, 55, 3813, 9510, 3474, 39016 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0....1....1....2.......3........5.........8.........13...........21

..1....7...14...33......70......157.......346........769.........1710

..1...14...22...34.....182......438.......920.......3431.........9510

..2...33...34...91.....352......372......1016.......3474.........4945

..3...70..182..352....3384....15814.....39016.....211725......1172982

..5..157..438..372...15814...101803....285422....3531950.....30133609

..8..346..920.1016...39016...285422....630306...12378708....108542087

.13..769.3431.3474..211725..3531950..12378708..219093711...4455522372

.21.1710.9510.4945.1172982.30133609.108542087.4455522372.154688671720

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

k=3: [order 14] for n>16

k=4: [order 19] for n>24

k=5: [order 97] for n>101

EXAMPLE

Some solutions for n=5 k=4

..0..1..0..0. .0..1..1..0. .0..1..1..0. .0..1..0..0. .0..1..1..1

..1..1..0..1. .1..1..1..1. .0..1..0..0. .1..0..1..1. .1..1..0..0

..1..1..1..1. .1..1..0..1. .0..0..0..0. .1..1..1..1. .1..1..1..0

..0..0..1..1. .1..0..1..1. .0..0..1..0. .1..1..0..1. .0..1..1..1

..1..0..1..0. .0..1..1..0. .1..1..0..0. .0..1..0..0. .0..0..1..0

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304143.

Sequence in context: A119506 A304149 A305489 * A316740 A304019 A305367

Adjacent sequences:  A305086 A305087 A305088 * A305090 A305091 A305092

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 25 2018

STATUS

approved

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Last modified December 5 06:05 EST 2021. Contains 349531 sequences. (Running on oeis4.)