A283100 T(n,k) = Number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements.

0, 0, 0, 0, 0, 0, 1, 6, 6, 1, 2, 28, 72, 28, 2, 5, 142, 600, 600, 142, 5, 13, 606, 4607, 8536, 4607, 606, 13, 29, 2458, 31669, 107007, 107007, 31669, 2458, 29, 65, 9520, 208949, 1237504, 2231690, 1237504, 208949, 9520, 65, 143, 35678, 1324269, 13563911

Offset

1,8

Comments

Table starts

..0.....0.......0..........1............2..............5...............13

..0.....0.......6.........28..........142............606.............2458

..0.....6......72........600.........4607..........31669...........208949

..1....28.....600.......8536.......107007........1237504.........13563911

..2...142....4607.....107007......2231690.......42681282........774403237

..5...606...31669....1237504.....42681282.....1354321470......40737147156

.13..2458..208949...13563911....774403237....40737147156....2028744947006

.29..9520.1324269..142827186..13508097744..1177012522158...97051820977159

.65.35678.8152245.1460284133.228643318057.32993790452893.4503103658479576

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -2*a(n-3) -6*a(n-4) +4*a(n-6) +6*a(n-7) +3*a(n-8) +a(n-9).

k=2: [order 12]

k=3: [order 27]

k=4: [order 46]

Example

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

Crossrefs

Column 1 is A282831.

Sequence in context: A322622 A176565 A176567 * A065493 A133890 A248059

Adjacent sequences: A283097 A283098 A283099 * A283101 A283102 A283103

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 28 2017

Status

approved