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A300182 T(n,k)=Number of nXk 0..1 arrays with every element equal 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, 2033, 2033, 512, 32, 64, 2048, 16208, 32321, 16208, 2048, 64, 128, 8192, 129217, 513832, 513832, 129217, 8192, 128, 256, 32768, 1030173, 8168705, 16288960, 8168705, 1030173, 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........2033..........16208...........129217

...8....128.....2033.......32321.........513832..........8168705

..16....512....16208......513832.......16288960........516368256

..32...2048...129217.....8168705......516368256......32640586945

..64...8192..1030173...129863167....16369174784....2063278351093

.128..32768..8212978..2064518282...518912313824..130424025161538

.256.131072.65477359.32820974441.16449820393120.8244367994118153

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..364

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) +6*a(n-3)

k=4: a(n) = 14*a(n-1) +27*a(n-2) +51*a(n-3) -10*a(n-4) -a(n-5) -10*a(n-6)

k=5: [order 9]

k=6: [order 15]

k=7: [order 36]

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A301407 A213418 A317517 * A317532 A222659 A116694

Adjacent sequences:  A300179 A300180 A300181 * A300183 A300184 A300185

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 27 2018

STATUS

approved

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Last modified January 23 22:16 EST 2020. Contains 331177 sequences. (Running on oeis4.)