A296827 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2, 3 or 4 king-move neighboring 1s.

1, 1, 1, 1, 6, 1, 1, 21, 21, 1, 1, 56, 94, 56, 1, 1, 178, 352, 352, 178, 1, 1, 609, 2133, 2272, 2133, 609, 1, 1, 1997, 11930, 24367, 24367, 11930, 1997, 1, 1, 6511, 60772, 214243, 510086, 214243, 60772, 6511, 1, 1, 21494, 326592, 1814475, 8721984, 8721984

Offset

1,5

Comments

Table starts

.1.....1.......1.........1...........1.............1................1

.1.....6......21........56.........178...........609.............1997

.1....21......94.......352........2133.........11930............60772

.1....56.....352......2272.......24367........214243..........1814475

.1...178....2133.....24367......510086.......8721984........139963008

.1...609...11930....214243.....8721984.....267542809.......7478283799

.1..1997...60772...1814475...139963008....7478283799.....364592446431

.1..6511..326592..16388418..2411616295..232289837440...20210620228470

.1.21494.1772900.145662798.41118326040.7106285417721.1091459884529060

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 3*a(n-1) +5*a(n-3) -2*a(n-4) -10*a(n-5) -8*a(n-6)

k=3: [order 16]

k=4: [order 35]

Example

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

Crossrefs

Sequence in context: A060972 A144066 A363849 * A056941 A157638 A347975

Adjacent sequences: A296824 A296825 A296826 * A296828 A296829 A296830

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 21 2017

Status

approved