A301407 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 252, 128, 16, 32, 512, 1988, 1988, 512, 32, 64, 2048, 15680, 31012, 15680, 2048, 64, 128, 8192, 123676, 483600, 483600, 123676, 8192, 128, 256, 32768, 975492, 7541492, 14905344, 7541492, 975492, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

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

...4.....32......252........1988..........15680...........123676

...8....128.....1988.......31012.........483600..........7541492

..16....512....15680......483600.......14905344........459428416

..32...2048...123676.....7541492......459428416......27990353344

..64...8192...975492...117605364....14160945920....1705287652128

.128..32768..7694176..1833990416...436482419456..103893157740576

.256.131072.60687676.28600063044.13453684678656.6329599807409536

Links

R. H. Hardin, Table of n, a(n) for n = 1..391

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)

k=4: a(n) = 13*a(n-1) +40*a(n-2) +9*a(n-3) -29*a(n-4) +4*a(n-5)

k=5: [order 8] for n>9

k=6: [order 22] for n>23

k=7: [order 45] for n>47

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A317525 A300208 A303421 * A213418 A317517 A300182

Adjacent sequences: A301404 A301405 A301406 * A301408 A301409 A301410

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 20 2018

Status

approved