A296739 T(n,k) = Number of n X k 0..1 arrays with each 1 adjacent to 1, 2 or 4 king-move neighboring 1's.

1, 2, 2, 4, 11, 4, 7, 31, 31, 7, 12, 88, 126, 88, 12, 21, 287, 575, 575, 287, 21, 37, 881, 2832, 4251, 2832, 881, 37, 65, 2686, 13322, 34086, 34086, 13322, 2686, 65, 114, 8347, 62874, 261354, 458494, 261354, 62874, 8347, 114, 200, 25763, 299056, 2009116

Offset

1,2

Comments

Table starts

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

...2....11......31........88.........287..........881...........2686

...4....31.....126.......575........2832........13322..........62874

...7....88.....575......4251.......34086.......261354........2009116

..12...287....2832.....34086......458494......5692727.......71592909

..21...881...13322....261354.....5692727....114153198.....2324267560

..37..2686...62874...2009116....71592909...2324267560....76925689840

..65..8347..299056..15561333...910873718..47816866681..2573555751062

.114.25763.1418177.120192735.11510112796.977475485051.85477431609556

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

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) +8*a(n-3) -12*a(n-4) +2*a(n-5) -12*a(n-6).

k=3: [order 16].

k=4: [order 35].

Example

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

Crossrefs

Column 1 is A005251(n+2).

Sequence in context: A196707 A196950 A295847 * A218823 A296599 A219106

Adjacent sequences: A296736 A296737 A296738 * A296740 A296741 A296742

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 19 2017

Status

approved