A296688 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s.

1, 2, 2, 4, 12, 4, 7, 43, 43, 7, 12, 145, 210, 145, 12, 21, 524, 1162, 1162, 524, 21, 37, 1888, 6959, 11478, 6959, 1888, 37, 65, 6737, 39608, 121477, 121477, 39608, 6737, 65, 114, 24093, 226599, 1210458, 2323514, 1210458, 226599, 24093, 114, 200, 86250

Offset

1,2

Comments

Table starts

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

...2....12......43........145..........524...........1888.............6737

...4....43.....210.......1162.........6959..........39608...........226599

...7...145....1162......11478.......121477........1210458.........12227803

..12...524....6959.....121477......2323514.......40828110........732185986

..21..1888...39608....1210458.....40828110.....1231267842......38342595769

..37..6737..226599...12227803....732185986....38342595769....2094245366560

..65.24093.1305725..124103052..13222385649..1202783176853..115207878553368

.114.86250.7497482.1254382781.237236541596.37385385800350.6267132000869767

Links

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

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) +11*a(n-3) -2*a(n-4) +8*a(n-5) -4*a(n-6)

k=3: [order 12]

k=4: [order 26]

k=5: [order 63]

Example

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

Crossrefs

Column 1 is A005251(n+2).

Sequence in context: A260878 A064880 A115011 * A219569 A202795 A256890

Adjacent sequences: A296685 A296686 A296687 * A296689 A296690 A296691

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 18 2017

Status

approved