A318045 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 8, 3, 1, 1, 6, 21, 21, 6, 1, 1, 17, 86, 140, 86, 17, 1, 1, 46, 377, 905, 905, 377, 46, 1, 1, 124, 1648, 6179, 10563, 6179, 1648, 124, 1, 1, 341, 7261, 42793, 116212, 116212, 42793, 7261, 341, 1, 1, 947, 31969, 297043, 1304057, 2098813

Offset

1,5

Comments

Table starts

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

.1...2.....2.......3.........6..........17...........46............124

.1...2.....8......21........86.........377.........1648...........7261

.1...3....21.....140.......905........6179........42793.........297043

.1...6....86.....905.....10563......116212......1304057.......14683085

.1..17...377....6179....116212.....2098813.....37826270......685931021

.1..46..1648...42793...1304057....37826270...1097286743....32035215365

.1.124..7261..297043..14683085...685931021..32035215365..1507709268026

.1.341.31969.2056698.165135266.12431437346.933917327711.70833352314014

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -a(n-2) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6) for n>7

k=3: [order 21] for n>23

k=4: [order 72] for n>74

Example

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

Crossrefs

Sequence in context: A241926 A174446 A071201 * A240656 A106476 A101566

Adjacent sequences: A318042 A318043 A318044 * A318046 A318047 A318048

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 13 2018

Status

approved