A296651 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 1 or 3 king-move neighboring 1s.

2, 4, 4, 7, 12, 7, 13, 29, 29, 13, 24, 85, 111, 85, 24, 44, 248, 468, 468, 248, 44, 81, 664, 1985, 3159, 1985, 664, 81, 149, 1897, 8126, 20782, 20782, 8126, 1897, 149, 274, 5385, 33933, 130303, 212537, 130303, 33933, 5385, 274, 504, 14924, 141664, 849983

Offset

1,1

Comments

Table starts

...2.....4......7.......13.........24...........44............81

...4....12.....29.......85........248..........664..........1897

...7....29....111......468.......1985.........8126.........33933

..13....85....468.....3159......20782.......130303........849983

..24...248...1985....20782.....212537......2022756......20337282

..44...664...8126...130303....2022756.....29547816.....453231742

..81..1897..33933...849983...20337282....453231742...10730354337

.149..5385.141664..5499124..202790850...6893592668..250993766141

.274.14924.588156.35347256.1998068553.103949473092.5814109226770

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +a(n-3)

k=2: a(n) = a(n-1) +3*a(n-2) +9*a(n-3) -4*a(n-4) -12*a(n-5) -4*a(n-6)

k=3: [order 10]

k=4: [order 22]

k=5: [order 58]

Example

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

Crossrefs

Column 1 is A000073(n+3).

Sequence in context: A227089 A225900 A227558 * A297085 A224158 A224409

Adjacent sequences: A296648 A296649 A296650 * A296652 A296653 A296654

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 17 2017

Status

approved