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A316808 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 247, 128, 16, 32, 512, 1905, 1905, 512, 32, 64, 2048, 14711, 28248, 14711, 2048, 64, 128, 8192, 113606, 420345, 420345, 113606, 8192, 128, 256, 32768, 877309, 6256258, 12075849, 6256258, 877309, 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......247........1905.........14711...........113606

...8....128.....1905.......28248........420345..........6256258

..16....512....14711......420345......12075849........347046960

..32...2048...113606.....6256258.....347046960......19261290694

..64...8192...877309....93109949....9972851339....1068884675914

.128..32768..6774916..1385723098..286582122564...59316329979368

.256.131072.52318510.20623265507.8235306627639.3291689981719718

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) -3*a(n-2) +7*a(n-3) -3*a(n-4)

k=4: a(n) = 15*a(n-1) -5*a(n-2) +50*a(n-3) -18*a(n-4) -81*a(n-5) +4*a(n-6) +20*a(n-7)

k=5: [order 22]

k=6: [order 59]

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A301443 A302010 A301784 * A299654 A317525 A300208

Adjacent sequences:  A316805 A316806 A316807 * A316809 A316810 A316811

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 14 2018

STATUS

approved

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Last modified September 25 09:46 EDT 2022. Contains 356977 sequences. (Running on oeis4.)