A304310 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 77, 65, 16, 32, 192, 261, 261, 192, 32, 64, 569, 918, 1137, 918, 569, 64, 128, 1709, 3270, 4979, 4979, 3270, 1709, 128, 256, 5162, 11739, 22089, 26548, 22089, 11739, 5162, 256, 512, 15663, 42286, 98560, 145369, 145369

Offset

1,2

Comments

Table starts

...1.....2......4.......8.......16........32.........64.........128

...2.....8.....23......65......192.......569.......1709........5162

...4....23.....77.....261......918......3270......11739.......42286

...8....65....261....1137.....4979.....22089......98560......441950

..16...192....918....4979....26548....145369.....795436.....4370971

..32...569...3270...22089...145369....989406....6692008....45578982

..64..1709..11739...98560...795436...6692008...55773947...469033247

.128..5162..42286..441950..4370971..45578982..469033247..4882896349

.256.15663.152593.1985853.24051887.310837633.3946132559.50824097741

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) = 3*a(n-1) +3*a(n-2) -6*a(n-3) -8*a(n-4) for n>5

k=3: [order 16]

k=4: [order 57] for n>59

Example

Some solutions for n=5 k=4
..0..1..1..0. .0..1..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..1
..1..1..1..1. .0..0..0..0. .0..1..0..1. .0..0..0..0. .1..1..1..0
..1..1..0..0. .0..0..0..0. .1..1..1..1. .0..1..1..1. .0..1..0..0
..1..1..0..0. .0..0..0..1. .1..1..1..0. .0..1..1..1. .0..0..0..0
..0..0..0..1. .1..0..1..1. .1..1..1..1. .0..1..1..1. .0..0..1..0

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A316289 A306053 A317230 * A316209 A305776 A317125

Adjacent sequences: A304307 A304308 A304309 * A304311 A304312 A304313

Keyword

nonn,tabl

Author

R. H. Hardin, May 10 2018

Status

approved