|
%I #14 Mar 31 2012 12:36:08
%S 16,81,21,256,83,42,625,205,277,61,1296,419,1098,367,106,2401,713,
%T 3265,1251,966,151,4096,1169,7988,3335,4895,1321,245,6561,1709,17119,
%U 7147,17608,5955,3078,359,10000,2471,33182,13411,50755,19617,20079,4553,567
%N T(n,m)=Number of (n+1)X2 0..m arrays with every 2X2 subblock commuting with each of its vertical 2X2 subblock neighbors
%C Table starts
%C ..16....81....256....625....1296....2401.....4096.....6561.....10000.....14641
%C ..21....83....205....419.....713....1169.....1709.....2471......3381......4543
%C ..42...277...1098...3265....7988...17119....33182....59629....100752....161981
%C ..61...367...1251...3335....7147...13411....23215....38239.....59909.....88585
%C .106...966...4895..17608...50755..125368...275175...553211...1033069...1819675
%C .151..1321...5955..19617...50359..110155...217601...401801....697077...1132921
%C .245..3078..20079..89163..306067..878507..2199713..4972138..10313788..19978800
%C .359..4553..27101.110707..340221..868467..1960451..4068951...7832237..14002123
%C .567.10028..84228.459455.1872721.6231024.17761659.45057701.103680616.220657654
%C .840.15650.123227.624228.2295521.6832034.17610501.41047301..87621283.172221291
%H R. H. Hardin, <a href="/A187363/b187363.txt">Table of n, a(n) for n = 1..2781</a>
%F 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))
%F 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
%e Some solutions for n=5 m=5
%e ..1..3....1..2....1..0....4..2....2..0....3..5....0..0....0..3....2..2....3..2
%e ..5..0....3..0....4..0....4..0....3..0....3..0....0..0....5..0....3..0....4..0
%e ..0..5....0..3....0..4....0..4....0..3....0..3....0..0....0..5....0..3....0..4
%e ..5..0....1..0....4..0....4..0....1..0....0..0....4..0....2..0....4..0....3..0
%e ..0..5....0..1....0..4....0..4....0..1....0..0....0..4....0..2....0..4....0..3
%e ..5..2....3..2....5..3....0..2....0..5....3..0....1..5....4..2....5..1....2..4
%Y Column 1 is A186454
%Y Column 2 is A186464
%Y Column 3 is A186474
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 24 2011
| 