A299721 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 46, 42, 1, 1, 127, 246, 246, 127, 1, 1, 389, 1205, 2545, 1205, 389, 1, 1, 1192, 6354, 23877, 23877, 6354, 1192, 1, 1, 3645, 33804, 242107, 439647, 242107, 33804, 3645, 1, 1, 11161, 182056, 2501312, 8668148, 8668148

Offset

1,5

Comments

Table starts

.1.....1......1.........1...........1..............1................1

.1.....5.....13........42.........127............389.............1192

.1....13.....46.......246........1205...........6354............33804

.1....42....246......2545.......23877.........242107..........2501312

.1...127...1205.....23877......439647........8668148........174287007

.1...389...6354....242107.....8668148......330958005......12889348273

.1..1192..33804...2501312...174287007....12889348273.....971255866215

.1..3645.182056..26078075..3523382014...504002310677...73433529818762

.1.11161.988181.273889895.71647565308.19818564264619.5581654300729422

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)

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

k=3: [order 12] for n>14

k=4: [order 29] for n>30

k=5: [order 83] for n>86

Example

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

Crossrefs

Column 2 is A298234.

Sequence in context: A299893 A299060 A299821 * A300342 A119725 A239279

Adjacent sequences: A299718 A299719 A299720 * A299722 A299723 A299724

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 17 2018

Status

approved