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

1,2

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

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) +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]

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A303456 A301443 A302010 * A316808 A299654 A317525

Adjacent sequences: A301781 A301782 A301783 * A301785 A301786 A301787

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 26 2018

Status

approved