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A300208 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 248, 128, 16, 32, 512, 1933, 1933, 512, 32, 64, 2048, 15070, 29561, 15070, 2048, 64, 128, 8192, 117494, 451996, 451996, 117494, 8192, 128, 256, 32768, 916061, 6912249, 13548425, 6912249, 916061, 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......248........1933..........15070...........117494

...8....128.....1933.......29561.........451996..........6912249

..16....512....15070......451996.......13548425........406228452

..32...2048...117494.....6912249......406228452......23883950854

..64...8192...916061...105708560....12180207076....1404241937017

.128..32768..7142233..1616600364...365209429387...82562348427139

.256.131072.55685704.24722667407.10950385677546.4854250928660105

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

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) -2*a(n-2) +5*a(n-3) -13*a(n-4) -6*a(n-5)

k=4: [order 15]

k=5: [order 38]

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A316808 A299654 A317525 * A303421 A301407 A213418

Adjacent sequences:  A300205 A300206 A300207 * A300209 A300210 A300211

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 28 2018

STATUS

approved

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Last modified September 19 11:23 EDT 2021. Contains 347556 sequences. (Running on oeis4.)