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A316815 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 227, 128, 16, 32, 512, 1603, 1603, 512, 32, 64, 2048, 11339, 19816, 11339, 2048, 64, 128, 8192, 80196, 246196, 246196, 80196, 8192, 128, 256, 32768, 567185, 3056047, 5391628, 3056047, 567185, 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................64

...2......8.......32........128...........512............2048..............8192

...4.....32......227.......1603.........11339...........80196............567185

...8....128.....1603......19816........246196.........3056047..........37935501

..16....512....11339.....246196.......5391628.......117897523........2578023456

..32...2048....80196....3056047.....117897523......4537910922......174669587289

..64...8192...567185...37935501....2578023456....174669587289....11834952392431

.128..32768..4011528..470942175...56382210217...6724877943937...802147875327622

.256.131072.28372197.5846244187.1233022160942.258886627124646.54360782611063950

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) = 4*a(n-1)

k=3: a(n) = 6*a(n-1) +10*a(n-2) -7*a(n-3) -64*a(n-4) -51*a(n-5) for n>6

k=4: [order 17] for n>18

k=5: [order 62] for n>63

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A298970 A316960 A299740 * A299661 A320371 A317565

Adjacent sequences:  A316812 A316813 A316814 * A316816 A316817 A316818

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 14 2018

STATUS

approved

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Last modified September 27 13:39 EDT 2020. Contains 337380 sequences. (Running on oeis4.)