A203181 T(n,k) is the number of n X k 0..2 arrays with every 1 immediately preceded by 0 to the left or above, no 0 immediately preceded by a 0, and every 2 immediately preceded by 0 1 to the left or above.

1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 4, 7, 4, 3, 4, 6, 17, 17, 6, 4, 5, 10, 41, 59, 41, 10, 5, 7, 18, 97, 205, 205, 97, 18, 7, 9, 30, 235, 724, 952, 724, 235, 30, 9, 12, 50, 607, 2466, 4654, 4654, 2466, 607, 50, 12, 16, 86, 1415, 8948, 23083, 32411, 23083, 8948, 1415, 86, 16, 21, 146

Offset

1,4

Comments

Table starts

.1..1...2....2......3.......4........5.........7..........9..........12

.1..1...2....4......6......10.......18........30.........50..........86

.2..2...7...17.....41......97......235.......607.......1415........3486

.2..4..17...59....205.....724.....2466......8948......30945......108083

.3..6..41..205....952....4654....23083....115377.....551208.....2757161

.4.10..97..724...4654...32411...223567...1625772...10889470....76035931

.5.18.235.2466..23083..223567..2208945..22411843..216858412..2141041521

.7.30.607.8948.115377.1625772.22411843.323885934.4389100997.61921804090

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Example

Some solutions for n=5 k=3
..0..1..0....0..1..2....0..1..0....0..1..0....0..1..2....0..1..0....0..1..2
..1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1
..2..1..2....2..1..0....2..1..2....0..1..0....0..1..2....0..1..2....0..1..0
..0..1..2....0..1..2....0..1..0....1..2..1....1..2..0....1..2..0....1..2..1
..1..0..1....1..0..1....1..0..1....2..0..1....0..1..1....0..1..1....2..0..1

Crossrefs

Column 1 is A000931(n+5). Column 2 is A203175.

Sequence in context: A105223 A025859 A031281 * A113793 A289499 A215904

Adjacent sequences: A203178 A203179 A203180 * A203182 A203183 A203184

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 30 2011

Status

approved