A298970 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 219, 128, 16, 32, 512, 1575, 1575, 512, 32, 64, 2048, 11283, 21098, 11283, 2048, 64, 128, 8192, 80972, 280468, 280468, 80972, 8192, 128, 256, 32768, 581057, 3740381, 6892031, 3740381, 581057, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

...1.....2.......4.........8...........16.............32...............64

...2.....8......32.......128..........512...........2048.............8192

...4....32.....219......1575........11283..........80972...........581057

...8...128....1575.....21098.......280468........3740381.........49885231

..16...512...11283....280468......6892031......170137416.......4200575252

..32..2048...80972...3740381....170137416.....7785598672.....356356552103

..64..8192..581057..49885231...4200575252...356356552103...30241030285680

.128.32768.4169867.665351771.103715870545.16312003284843.2566506415636896

Links

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

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 4*a(n-1)

k=3: [order 8]

k=4: [order 23]

k=5: [order 75]

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A299668 A300259 A305523 * A316960 A299740 A316815

Adjacent sequences: A298967 A298968 A298969 * A298971 A298972 A298973

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 30 2018

Status

approved