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

Author

R. H. Hardin, Feb 27 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

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]