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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. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)