A282838 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly two elements.

0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 16, 18, 16, 2, 5, 32, 201, 201, 32, 5, 13, 144, 1019, 2376, 1019, 144, 13, 29, 544, 6472, 17965, 17965, 6472, 544, 29, 65, 1664, 34464, 151084, 215304, 151084, 34464, 1664, 65, 143, 5664, 176355, 1172252, 2839946, 2839946

Offset

1,11

Comments

Table starts

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

...0.....0.......0........16..........32...........144.............544

...0.....0......18.......201........1019..........6472...........34464

...1....16.....201......2376.......17965........151084.........1172252

...2....32....1019.....17965......215304.......2839946........33527252

...5...144....6472....151084.....2839946......54433534.......957808843

..13...544...34464...1172252....33527252.....957808843.....25269280218

..29..1664..176355...8673640...380934118...16264638662....643705916373

..65..5664..887369..63747749..4251423677..270202982809..16010099108460

.143.17968.4302058.455684388.46024376400.4371000525304.388020733786517

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 9]

k=3: [order 18]

k=4: [order 27]

k=5: [order 63]

k=6: [order 90]

Example

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

Crossrefs

Sequence in context: A368404 A217307 A282408 * A180923 A058242 A101075

Adjacent sequences: A282835 A282836 A282837 * A282839 A282840 A282841

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 22 2017

Status

approved