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

Author

R. H. Hardin Mar 24 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A186454

Column 2 is A186464

Column 3 is A186474

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