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

1,5

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

Links

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

Example

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

Crossrefs

Diagonal is A145857

Column 2 is A000930(n+1)

Column 3 is A003229

Sequence in context: A297845 A183456 A296313 * A046688 A208342 A157283

Adjacent sequences: A183339 A183340 A183341 * A183343 A183344 A183345

Keyword

nonn,tabl

Author

R. H. Hardin Jan 04 2011

Status

approved