A300182 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 255, 128, 16, 32, 512, 2033, 2033, 512, 32, 64, 2048, 16208, 32321, 16208, 2048, 64, 128, 8192, 129217, 513832, 513832, 129217, 8192, 128, 256, 32768, 1030173, 8168705, 16288960, 8168705, 1030173, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

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

...4.....32......255........2033..........16208...........129217

...8....128.....2033.......32321.........513832..........8168705

..16....512....16208......513832.......16288960........516368256

..32...2048...129217.....8168705......516368256......32640586945

..64...8192..1030173...129863167....16369174784....2063278351093

.128..32768..8212978..2064518282...518912313824..130424025161538

.256.131072.65477359.32820974441.16449820393120.8244367994118153

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

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

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

k=3: a(n) = 7*a(n-1) +7*a(n-2) +6*a(n-3)

k=4: a(n) = 14*a(n-1) +27*a(n-2) +51*a(n-3) -10*a(n-4) -a(n-5) -10*a(n-6)

k=5: [order 9]

k=6: [order 15]

k=7: [order 36]

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A301407 A213418 A317517 * A317532 A222659 A116694

Adjacent sequences: A300179 A300180 A300181 * A300183 A300184 A300185

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 27 2018

Status

approved