A187363 T(n,m)=Number of (n+1)X2 0..m arrays with every 2X2 subblock commuting with each of its vertical 2X2 subblock neighbors

16, 81, 21, 256, 83, 42, 625, 205, 277, 61, 1296, 419, 1098, 367, 106, 2401, 713, 3265, 1251, 966, 151, 4096, 1169, 7988, 3335, 4895, 1321, 245, 6561, 1709, 17119, 7147, 17608, 5955, 3078, 359, 10000, 2471, 33182, 13411, 50755, 19617, 20079, 4553, 567

Offset

1,1

Comments

Table starts

..16....81....256....625....1296....2401.....4096.....6561.....10000.....14641

..21....83....205....419.....713....1169.....1709.....2471......3381......4543

..42...277...1098...3265....7988...17119....33182....59629....100752....161981

..61...367...1251...3335....7147...13411....23215....38239.....59909.....88585

.106...966...4895..17608...50755..125368...275175...553211...1033069...1819675

.151..1321...5955..19617...50359..110155...217601...401801....697077...1132921

.245..3078..20079..89163..306067..878507..2199713..4972138..10313788..19978800

.359..4553..27101.110707..340221..868467..1960451..4068951...7832237..14002123

.567.10028..84228.459455.1872721.6231024.17761659.45057701.103680616.220657654

.840.15650.123227.624228.2295521.6832034.17610501.41047301..87621283.172221291

Links

R. H. Hardin, Table of n, a(n) for n = 1..2781

Formula

Empirical for column m: a(n)=2*a(n-1)+(m-1)*a(n-2)-2*m*a(n-3)+2*m*a(n-4)-m*a(n-5) for n>(6+2*A072649(m))

Empirical more generally for column m of T(n,m,k) for (n+1)X(k+1) 0..m arrays: a(n)=2*a(n-1)+(m-1)*a(n-2)-2*m*a(n-3)+2*m*a(n-4)-m*a(n-5) for n>(k+5+2*A072649(m)), except n>(k+4+2*A072649(m)) for m=1 and k>1

Example

Some solutions for n=5 m=5
..1..3....1..2....1..0....4..2....2..0....3..5....0..0....0..3....2..2....3..2
..5..0....3..0....4..0....4..0....3..0....3..0....0..0....5..0....3..0....4..0
..0..5....0..3....0..4....0..4....0..3....0..3....0..0....0..5....0..3....0..4
..5..0....1..0....4..0....4..0....1..0....0..0....4..0....2..0....4..0....3..0
..0..5....0..1....0..4....0..4....0..1....0..0....0..4....0..2....0..4....0..3
..5..2....3..2....5..3....0..2....0..5....3..0....1..5....4..2....5..1....2..4

Crossrefs

Column 1 is A186454

Column 2 is A186464

Column 3 is A186474

Sequence in context: A005065 A056553 A053167 * A361266 A110892 A202880

Adjacent sequences: A187360 A187361 A187362 * A187364 A187365 A187366

Keyword

nonn,tabl

Author

R. H. Hardin Mar 24 2011

Status

approved