A281034 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than three of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 12, 96, 12, 0, 0, 58, 532, 532, 58, 0, 0, 252, 2321, 2324, 2321, 252, 0, 0, 1048, 8886, 9854, 9854, 8886, 1048, 0, 0, 4204, 31700, 38972, 44395, 38972, 31700, 4204, 0, 0, 16454, 108034, 146606, 184290, 184290, 146606, 108034, 16454, 0

Offset

1,8

Comments

Table starts

.0.....0.......0.......0........0.........0.........0..........0..........0

.0.....0.......2......12.......58.......252......1048.......4204......16454

.0.....2......96.....532.....2321......8886.....31700.....108034.....357542

.0....12.....532....2324.....9854.....38972....146606.....533340....1896352

.0....58....2321....9854....44395....184290....722952....2696692....9734320

.0...252....8886...38972...184290....770788...3042556...11471132...41949794

.0..1048...31700..146606...722952...3042556..12164474...46511454..172759149

.0..4204..108034..533340..2696692..11471132..46511454..180119924..677915790

.0.16454..357542.1896352..9734320..41949794.172759149..677915790.2586759715

.0.63236.1158596.6625144.34378916.150344672.628675456.2501817200.9677601094

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: [order 10]

k=3: [order 18] for n>21

k=4: [order 36] for n>41

k=5: [order 98] for n>109

Example

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

Crossrefs

Sequence in context: A352661 A283494 A353254 * A282441 A281988 A190389

Adjacent sequences: A281031 A281032 A281033 * A281035 A281036 A281037

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 13 2017

Status

approved