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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. 7
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 (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......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

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Last modified October 20 10:43 EDT 2021. Contains 348100 sequences. (Running on oeis4.)