A299060 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 38, 42, 1, 1, 127, 199, 199, 127, 1, 1, 389, 864, 2096, 864, 389, 1, 1, 1192, 4366, 17930, 17930, 4366, 1192, 1, 1, 3645, 21804, 175031, 295407, 175031, 21804, 3645, 1, 1, 11161, 111861, 1718789, 5558665, 5558665

Offset

1,5

Comments

Table starts

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

.1....5.....13.......42........127..........389...........1192.............3645

.1...13.....38......199........864.........4366..........21804...........111861

.1...42....199.....2096......17930.......175031........1718789.........17101477

.1..127....864....17930.....295407......5558665......104819165.......1992248544

.1..389...4366...175031....5558665....199153610.....7165136807.....259511787831

.1.1192..21804..1718789..104819165...7165136807...491688804213...33934925502793

.1.3645.111861.17101477.1992248544.259511787831.33934925502793.4462148033879670

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 14] for n>16

k=4: [order 38] for n>39

Example

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

Crossrefs

Column 2 is A298234.

Sequence in context: A299366 A299135 A299893 * A299821 A299721 A300342

Adjacent sequences: A299057 A299058 A299059 * A299061 A299062 A299063

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 01 2018

Status

approved