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.

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

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