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.

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

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