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A317572 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 30, 30, 8, 16, 112, 170, 112, 16, 32, 420, 997, 997, 420, 32, 64, 1576, 5837, 9513, 5837, 1576, 64, 128, 5912, 34152, 91461, 91461, 34152, 5912, 128, 256, 22176, 199987, 869466, 1489357, 869466, 199987, 22176, 256, 512, 83184, 1170900 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1.....2.......4.........8..........16.............32...............64

...2.....8......30.......112.........420...........1576.............5912

...4....30.....170.......997........5837..........34152...........199987

...8...112.....997......9513.......91461.........869466..........8305672

..16...420....5837.....91461.....1489357.......23570355........376898848

..32..1576...34152....869466....23570355......611929512......16121282196

..64..5912..199987...8305672...376898848....16121282196.....703696012516

.128.22176.1170900..79320881..6024751866...424656152144...30722175114871

.256.83184.6855565.757097096.96177867099.11163587715218.1337502015395808

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3)

k=3: [order 11] for n>12

k=4: [order 38] for n>39

EXAMPLE

Some solutions for n=5 k=4

..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..1

..1..0..0..0. .1..0..1..0. .1..0..0..0. .0..0..0..1. .1..0..0..1

..0..0..0..1. .0..1..1..1. .0..0..0..1. .0..0..0..1. .1..0..1..0

..1..1..1..0. .0..1..0..0. .0..0..0..1. .0..1..0..0. .0..1..0..0

..0..0..0..0. .0..1..1..1. .1..0..0..1. .0..0..1..0. .1..1..0..1

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A281949.

Sequence in context: A305530 A317004 A316822 * A281837 A299081 A299844

Adjacent sequences:  A317569 A317570 A317571 * A317573 A317574 A317575

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 31 2018

STATUS

approved

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Last modified November 27 03:56 EST 2021. Contains 349345 sequences. (Running on oeis4.)