A295847 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 2 king-move neighboring 1s.

1, 2, 2, 4, 11, 4, 7, 29, 29, 7, 12, 80, 104, 80, 12, 21, 261, 467, 467, 261, 21, 37, 789, 2197, 3472, 2197, 789, 37, 65, 2354, 9645, 26544, 26544, 9645, 2354, 65, 114, 7199, 43335, 190943, 333366, 190943, 43335, 7199, 114, 200, 21889, 195508, 1406191

Offset

1,2

Comments

Table starts

...1.....2......4........7.........12...........21.............37

...2....11.....29.......80........261..........789...........2354

...4....29....104......467.......2197.........9645..........43335

...7....80....467.....3472......26544.......190943........1406191

..12...261...2197....26544.....333366......3804661.......45214991

..21...789...9645...190943....3804661.....68406015.....1296880337

..37..2354..43335..1406191...45214991...1296880337....39611268638

..65..7199.195508.10368395..538013975..24467737897..1200659717965

.114.21889.876170.76065766.6343699611.457692634063.36061398110075

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

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

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

k=3: [order 9]

k=4: [order 16]

k=5: [order 35]

k=6: [order 73]

Example

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

Crossrefs

Column 1 is A005251(n+2).

Sequence in context: A196856 A196707 A196950 * A296739 A218823 A296599

Adjacent sequences: A295844 A295845 A295846 * A295848 A295849 A295850

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2017

Status

approved