A281563 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal 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, 1, 0, 0, 18, 68, 6, 0, 0, 141, 621, 815, 57, 0, 0, 602, 2426, 3374, 4172, 310, 0, 0, 2180, 6955, 12133, 15508, 18020, 1508, 0, 0, 7006, 16656, 31300, 50510, 53568, 62882, 6854, 0, 0, 20979, 36578, 67834, 119319, 154722, 162919, 201551

Offset

1,8

Comments

Table starts

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

.0......0.......5......18.....141......602.....2180.....7006....20979.....59698

.0......1......68.....621....2426.....6955....16656....36578....76332....153813

.0......6.....815....3374...12133....31300....67834...136056...264286....498750

.0.....57....4172...15508...50510...119319...243040...458646...836348...1499031

.0....310...18020...53568..154722...347316...692421..1275888..2241388...3864672

.0...1508...62882..162919..430995...919632..1818257..3326246..5744641...9601436

.0...6854..201551..463916.1166392..2383814..4578736..8300608.14212419..23352928

.0..29487..605398.1262057.3018274..5976640.11105124.19678234.33449458..54649755

.0.122326.1743548.3344312.7606230.14598286.26461889.45643798.76274137.124061416

Links

R. H. Hardin, Table of n, a(n) for n = 1..242

Formula

Empirical for column k:

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

k=2: [order 12]

k=3: [order 21] for n>29

k=4: [order 24] for n>34

k=5: [order 29] for n>46

k=6: [order 32] for n>52

k=7: [order 35] for n>58

Empirical for row n:

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

n=2: [order 14] for n>15

n=3: [order 12] for n>20

n=4: [order 15] for n>24

n=5: [order 18] for n>28

n=6: [order 21] for n>37

n=7: [order 24] for n>46

Example

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

Crossrefs

Sequence in context: A204170 A283784 A361353 * A293087 A209349 A242095

Adjacent sequences: A281560 A281561 A281562 * A281564 A281565 A281566

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 24 2017

Status

approved