A183342 T(n,k)=Number of nXk binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 4, 1, 1, 6, 7, 7, 6, 1, 1, 9, 13, 12, 13, 9, 1, 1, 13, 23, 26, 26, 23, 13, 1, 1, 19, 37, 51, 72, 51, 37, 19, 1, 1, 28, 63, 97, 175, 175, 97, 63, 28, 1, 1, 41, 109, 193, 407, 513, 407, 193, 109, 41, 1, 1, 60, 183, 380, 1005, 1397, 1397, 1005, 380

Offset: 1

Author

R. H. Hardin Jan 04 2011

Keywords

• nonn
• tabl

Comments

Equivalent to all 1s connected only in 2X2 blocks

Table starts

.1..1...1...1....1.....1......1.......1.......1........1.........1..........1

.1..2...3...4....6.....9.....13......19......28.......41........60.........88

.1..3...5...7...13....23.....37......63.....109......183.......309........527

.1..4...7..12...26....51.....97.....193.....380......741......1456.......2860

.1..6..13..26...72...175....407....1005....2450.....5893.....14318......34780

.1..9..23..51..175...513...1397....4133...12075....34521....100047.....290287

.1.13..37..97..407..1397...4531...16029...55471...188735....651517....2246015

.1.19..63.193.1005..4133..16029...68662..286079..1170324...4869491...20218182

.1.28.109.380.2450.12075..55471..286079.1429824..6989477..34856362..173451524

.1.41.183.741.5893.34521.188735.1170324.6989477.40840428.243887497.1451641573

Examples

			Some solutions for 6X5
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..1..1..0....1..1..0..0..0....0..0..0..0..0
..0..0..1..1..0....0..0..1..1..0....1..1..0..0..0....0..0..0..0..0
..0..0..1..1..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....1..1..0..0..0....0..0..0..0..0....0..1..1..0..0
..0..0..0..0..0....1..1..0..0..0....0..0..0..0..0....0..1..1..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..839

Crossrefs

Diagonal is A145857

Column 2 is A000930(n+1)

Column 3 is A003229