A298328 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 12, 12, 1, 1, 37, 22, 37, 1, 1, 104, 78, 78, 104, 1, 1, 301, 283, 382, 283, 301, 1, 1, 864, 1097, 1998, 1998, 1097, 864, 1, 1, 2485, 4503, 11727, 17984, 11727, 4503, 2485, 1, 1, 7144, 18491, 73321, 170318, 170318, 73321, 18491, 7144, 1, 1, 20541

Offset

1,5

Comments

Table starts

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

.1....5....12......37.......104.........301..........864...........2485

.1...12....22......78.......283........1097.........4503..........18491

.1...37....78.....382......1998.......11727........73321.........464117

.1..104...283....1998.....17984......170318......1664958.......16189372

.1..301..1097...11727....170318.....2614097.....41029614......638898386

.1..864..4503...73321...1664958....41029614...1019874462....25083063173

.1.2485.18491..464117..16189372...638898386..25083063173...970377749534

.1.7144.77067.2989370.158726938.10052063678.624245464335.38070771240926

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) = 5*a(n-2) +8*a(n-3) +4*a(n-4)

k=3: [order 19] for n>20

k=4: [order 67] for n>68

Example

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

Crossrefs

Column 2 is A297909.

Sequence in context: A146987 A297915 A298508 * A299221 A300035 A130227

Adjacent sequences: A298325 A298326 A298327 * A298329 A298330 A298331

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 17 2018

Status

approved