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A318222 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 4, 2, 0, 0, 5, 18, 18, 5, 0, 0, 16, 86, 174, 86, 16, 0, 0, 45, 413, 1538, 1538, 413, 45, 0, 0, 123, 1975, 13722, 24576, 13722, 1975, 123, 0, 0, 340, 9474, 123415, 407121, 407121, 123415, 9474, 340, 0, 0, 946, 45415, 1108310, 6735734 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

Table starts

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

.0...1.....1.......2..........5...........16.............45...............123

.0...1.....4......18.........86..........413...........1975..............9474

.0...2....18.....174.......1538........13722.........123415...........1108310

.0...5....86....1538......24576.......407121........6735734.........111410550

.0..16...413...13722.....407121.....12458503......381426500.......11669008142

.0..45..1975..123415....6735734....381426500....21578384304.....1220340668071

.0.123..9474.1108310..111410550..11669008142..1220340668071...127593300875084

.0.340.45415.9952342.1842642459.357007586982.69013808316210.13340146521225527

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

FORMULA

Empirical for column k:

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

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

k=3: [order 11]

k=4: [order 36] for n>39

EXAMPLE

Some solutions for n=5 k=4

..0..1..1..0. .0..1..0..0. .0..1..0..1. .0..1..0..0. .0..1..0..1

..1..0..0..1. .1..0..1..1. .1..1..0..1. .1..0..1..1. .1..1..1..0

..0..1..1..0. .1..0..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..1

..0..0..1..1. .0..1..0..1. .1..1..1..0. .0..0..0..1. .1..1..1..0

..1..0..1..0. .0..1..1..0. .0..0..0..1. .1..1..1..0. .0..1..0..1

CROSSREFS

Column 2 is A317890.

Sequence in context: A278215 A317896 A320364 * A209466 A277659 A331144

Adjacent sequences:  A318219 A318220 A318221 * A318223 A318224 A318225

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 21 2018

STATUS

approved

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Last modified September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)