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A317611 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 38, 28, 16, 32, 94, 109, 109, 94, 32, 64, 284, 419, 472, 419, 284, 64, 128, 752, 1413, 2639, 2639, 1413, 752, 128, 256, 2244, 4708, 13134, 23031, 13134, 4708, 2244, 256, 512, 6532, 16406, 64593, 161091, 161091, 64593 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1....2.....4.......8.......16.........32..........64...........128

...2....4....14......28.......94........284.........752..........2244

...4...14....38.....109......419.......1413........4708.........16406

...8...28...109.....472.....2639......13134.......64593........329236

..16...94...419....2639....23031.....161091.....1160029.......8965243

..32..284..1413...13134...161091....1624676....17100005.....193630364

..64..752..4708...64593..1160029...17100005...271661553....4668181991

.128.2244.16406..329236..8965243..193630364..4668181991..124728567511

.256.6532.56424.1675126.67933591.2178634452.80648172452.3358612290228

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) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 61] for n>63

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A305911 A317153 A316883 * A220461 A220287 A320195

Adjacent sequences:  A317608 A317609 A317610 * A317612 A317613 A317614

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 01 2018

STATUS

approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)