A295040 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.

1, 2, 2, 4, 10, 4, 7, 29, 29, 7, 12, 87, 140, 87, 12, 21, 280, 741, 741, 280, 21, 37, 876, 3853, 6686, 3853, 876, 37, 65, 2735, 19956, 59126, 59126, 19956, 2735, 65, 114, 8583, 104096, 528282, 898493, 528282, 104096, 8583, 114, 200, 26900, 541775, 4738235

Offset: 1

Author

R. H. Hardin, Nov 12 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

...2....10......29........87.........280...........876............2735

...4....29.....140.......741........3853.........19956..........104096

...7....87.....741......6686.......59126........528282.........4738235

..12...280....3853.....59126......898493......13706771.......209181266

..21...876...19956....528282....13706771.....355281224......9248214732

..37..2735..104096...4738235...209181266....9248214732....411280569141

..65..8583..541775..42321441..3184995895..240292442848..18227207589288

.114.26900.2819027.378112132.48548926944.6243986963713.807975522778623

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..287

Crossrefs

Column 1 is A005251(n+2).

Column 2 is A295525.

Formula

Empirical for column k:

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

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

k=3: [order 15]

k=4: [order 34]

k=5: [order 91]