A297085 T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 2 king-move neighboring 1s.

2, 4, 4, 7, 12, 7, 13, 30, 30, 13, 24, 96, 136, 96, 24, 44, 286, 687, 687, 286, 44, 81, 848, 3616, 6784, 3616, 848, 81, 149, 2620, 19277, 64819, 64819, 19277, 2620, 149, 274, 7964, 105494, 654120, 1180260, 654120, 105494, 7964, 274, 504, 24332, 581688

Offset

1,1

Comments

Table starts

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

...4....12......30........96..........286............848..............2620

...7....30.....136.......687.........3616..........19277............105494

..13....96.....687......6784........64819.........654120...........6743851

..24...286....3616.....64819......1180260.......22630723.........444282892

..44...848...19277....654120.....22630723......833228038.......31284950414

..81..2620..105494...6743851....444282892....31284950414.....2245841563645

.149..7964..581688..69857453...8764056739..1180379285603...161959380452328

.274.24332.3225186.727765313.173651084724.44714930487805.11725115199949679

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +4*a(n-2) +4*a(n-3) -14*a(n-4) -14*a(n-5) -4*a(n-6)

k=3: [order 17]

k=4: [order 34]

Example

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

Crossrefs

Column 1 is A000073(n+3).

Sequence in context: A225900 A227558 A296651 * A224158 A224409 A226870

Adjacent sequences: A297082 A297083 A297084 * A297086 A297087 A297088

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 25 2017

Status

approved