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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 3
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A110892 A202880 A339596

Adjacent sequences:  A187360 A187361 A187362 * A187364 A187365 A187366

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 24 2011

STATUS

approved

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Last modified October 23 19:26 EDT 2021. Contains 348215 sequences. (Running on oeis4.)