A300096 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 7, 18, 1, 1, 31, 19, 19, 31, 1, 1, 65, 35, 56, 35, 65, 1, 1, 130, 95, 203, 203, 95, 130, 1, 1, 253, 225, 672, 1301, 672, 225, 253, 1, 1, 519, 575, 2168, 5953, 5953, 2168, 575, 519, 1, 1, 1018, 1563, 7287, 27614, 43848, 27614, 7287, 1563

Offset

1,5

Comments

Table starts

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

.1...5....7....18.....31.......65.......130.........253..........519

.1...7....7....19.....35.......95.......225.........575.........1563

.1..18...19....56....203......672......2168........7287........25652

.1..31...35...203...1301.....5953.....27614......144519.......776608

.1..65...95...672...5953....43848....310762.....2373454.....19198301

.1.130..225..2168..27614...310762...3273425....36840985....436133886

.1.253..575..7287.144519..2373454..36840985...616964357..10746198229

.1.519.1563.25652.776608.19198301.436133886.10746198229.279529477217

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 19] for n>20

k=4: [order 71] for n>72

Example

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

Crossrefs

Column 2 is A297937.

Sequence in context: A298382 A299249 A299458 * A294296 A078181 A054110

Adjacent sequences: A300093 A300094 A300095 * A300097 A300098 A300099

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 24 2018

Status

approved