A296039 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2 or 4 king-move neighboring 1s.

1, 1, 1, 1, 5, 1, 1, 11, 11, 1, 1, 21, 31, 21, 1, 1, 55, 70, 70, 55, 1, 1, 125, 251, 204, 251, 125, 1, 1, 271, 799, 997, 997, 799, 271, 1, 1, 645, 2266, 4102, 8472, 4102, 2266, 645, 1, 1, 1479, 7005, 15399, 51941, 51941, 15399, 7005, 1479, 1, 1, 3325, 21780, 63267

Offset

1,5

Comments

Table starts

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

.1....5....11.....21.......55.......125........271..........645..........1479

.1...11....31.....70......251.......799.......2266.........7005.........21780

.1...21....70....204......997......4102......15399........63267........258493

.1...55...251....997.....8472.....51941.....285366......1853852......11570787

.1..125...799...4102....51941....472540....3650122.....33758793.....307234618

.1..271..2266..15399...285366...3650122...39608385....518787061....6686146382

.1..645..7005..63267..1853852..33758793..518787061..10042412853..188033223758

.1.1479.21780.258493.11570787.307234618.6686146382.188033223758.5131681923323

Links

R. H. Hardin, Table of n, a(n) for n = 1..240

Formula

Empirical for column k:

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

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

k=3: [order 11]

k=4: [order 17]

k=5: [order 55]

Example

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

Crossrefs

Sequence in context: A132787 A181370 A119307 * A296974 A146954 A174949

Adjacent sequences: A296036 A296037 A296038 * A296040 A296041 A296042

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 03 2017

Status

approved