A301784 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 240, 128, 16, 32, 512, 1808, 1808, 512, 32, 64, 2048, 13616, 25872, 13616, 2048, 64, 128, 8192, 102544, 369936, 369936, 102544, 8192, 128, 256, 32768, 772272, 5289488, 10033408, 5289488, 772272, 32768, 256, 512, 131072

Offset: 1

Author

R. H. Hardin, Mar 26 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

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

...4.....32......240........1808.........13616...........102544

...8....128.....1808.......25872........369936..........5289488

..16....512....13616......369936......10033408........272151040

..32...2048...102544.....5289488.....272151040......14004742144

..64...8192...772272....75632400....7381982784.....720677122368

.128..32768..5816080..1081436176..200232929792...37085631944448

.256.131072.43801648.15463010576.5431228387584.1908405940870656

Examples

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

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) +4*a(n-2)

k=4: a(n) = 13*a(n-1) +20*a(n-2) -16*a(n-3) -64*a(n-4)

k=5: [order 8]

k=6: [order 20]

k=7: [order 46]