A317525 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 248, 128, 16, 32, 512, 1921, 1921, 512, 32, 64, 2048, 14892, 28760, 14892, 2048, 64, 128, 8192, 115446, 431529, 431529, 115446, 8192, 128, 256, 32768, 894961, 6475106, 12547746, 6475106, 894961, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

...1......2........4...........8............16...............32

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

...4.....32......248........1921.........14892...........115446

...8....128.....1921.......28760........431529..........6475106

..16....512....14892......431529......12547746........364882328

..32...2048...115446.....6475106.....364882328......20564214798

..64...8192...894961....97158833...10610584063....1158965686460

.128..32768..6937925..1457871738..308552557709...65318143510572

.256.131072.53784248.21875422403.8972619323210.3681268128789010

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

k=4: a(n) = 15*a(n-1) +a(n-2) -8*a(n-3) -84*a(n-4) -63*a(n-5) +24*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..1. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
..1..1..1..0. .1..1..0..1. .1..1..0..1. .0..0..0..1. .0..1..0..0
..1..0..0..1. .1..0..1..0. .1..0..0..0. .1..1..0..0. .0..0..0..0
..1..1..0..1. .1..0..1..0. .1..1..0..0. .0..1..1..0. .1..1..0..0
..1..1..0..0. .0..1..1..1. .0..0..1..1. .0..1..1..1. .0..0..1..1

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A301784 A316808 A299654 * A300208 A303421 A301407

Adjacent sequences: A317522 A317523 A317524 * A317526 A317527 A317528

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 30 2018

Status

approved