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.

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

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