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A317517 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 255, 128, 16, 32, 512, 2032, 2032, 512, 32, 64, 2048, 16193, 32256, 16193, 2048, 64, 128, 8192, 129042, 512096, 512096, 129042, 8192, 128, 256, 32768, 1028335, 8130048, 16198017, 8130048, 1028335, 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......255........2032..........16193...........129042

...8....128.....2032.......32256.........512096..........8130048

..16....512....16193......512096.......16198017........512358002

..32...2048...129042.....8130048......512358002......32289056648

..64...8192..1028335...129072576....16206294085....2034862700902

.128..32768..8194796..2049155072...512618027974..128237436273216

.256.131072.65304285.32532368768.16214518668763.8081548422775938

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..420

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) -a(n-2) +6*a(n-3)

k=4: a(n) = 16*a(n-1) -6*a(n-2) +64*a(n-3)

k=5: [order 8]

k=6: [order 15]

k=7: [order 34]

EXAMPLE

Some solutions for n=5 k=4

..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A303421 A301407 A213418 * A300182 A317532 A222659

Adjacent sequences:  A317514 A317515 A317516 * A317518 A317519 A317520

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 30 2018

STATUS

approved

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Last modified June 18 18:17 EDT 2021. Contains 345120 sequences. (Running on oeis4.)