A281165 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 two elements, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 18, 40, 18, 0, 0, 85, 477, 477, 85, 0, 0, 346, 3237, 4744, 3237, 346, 0, 0, 1388, 17806, 27229, 27229, 17806, 1388, 0, 0, 5454, 84443, 136138, 163762, 136138, 84443, 5454, 0, 0, 21171, 363824, 619502, 865821, 865821, 619502, 363824

Offset

1,8

Comments

Table starts

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

.0.....0.......5.......18........85........346.......1388........5454

.0.....5......40......477......3237......17806......84443......363824

.0....18.....477.....4744.....27229.....136138.....619502.....2648442

.0....85....3237....27229....163762.....865821....4098895....18213313

.0...346...17806...136138....865821....4716420...22796763...102696802

.0..1388...84443...619502...4098895...22796763..111826676...511077328

.0..5454..363824..2648442..18213313..102696802..511077328..2367603544

.0.21171.1461206.10801150..76987169..438513869.2213577238.10381031459

.0.81250.5575913.42551822.312665502.1799338352.9219387478.43770186654

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

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

k=2: [order 15]

k=3: [order 27] for n>32

k=4: [order 54] for n>61

Example

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

Crossrefs

Sequence in context: A285070 A285288 A356116 * A282481 A286979 A030047

Adjacent sequences: A281162 A281163 A281164 * A281166 A281167 A281168

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 16 2017

Status

approved