A301443 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 232, 128, 16, 32, 512, 1708, 1708, 512, 32, 64, 2048, 12576, 23672, 12576, 2048, 64, 128, 8192, 92616, 327848, 327848, 92616, 8192, 128, 256, 32768, 682084, 4543028, 8525992, 4543028, 682084, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

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

...4.....32......232........1708.........12576............92616

...8....128.....1708.......23672........327848..........4543028

..16....512....12576......327848.......8525992........221935656

..32...2048....92616.....4543028.....221935656......10857946336

..64...8192...682084....62956480....5777358820.....531234388944

.128..32768..5023328...872451104..150397035552...25991845818768

.256.131072.36995208.12090455460.3915165237488.1271713349901092

Links

R. H. Hardin, Table of n, a(n) for n = 1..286

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) = 8*a(n-1) -4*a(n-2) -5*a(n-3);

k=4: [order 11];

k=5: [order 31];

k=6: [order 97] for n>98.

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A300215 A300804 A303456 * A302010 A301784 A316808

Adjacent sequences: A301440 A301441 A301442 * A301444 A301445 A301446

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 21 2018

Status

approved