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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 17 03:53 EDT 2022. Contains 356184 sequences. (Running on oeis4.)