|
%I #5 Mar 31 2012 12:36:05
%S 4096,1709,1709,33182,4834,33182,23215,9789,9789,23215,275175,49867,
%T 269126,49867,275175,217601,91096,144828,144828,91096,217601,2199713,
%U 383152,2196353,1024481,2196353,383152,2199713,1960451,740408,1359050
%N T(n,k)=Number of (n+1)X(k+1) 0..7 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors
%C Table starts
%C .....4096.....1709.....33182.....23215.....275175.....217601.....2199713
%C .....1709.....4834......9789.....49867......91096.....383152......740408
%C ....33182.....9789....269126....144828....2196353....1359050....17630852
%C ....23215....49867....144828...1024481....1510299....8146732....11226859
%C ...275175....91096...2196353...1510299...21122896...11602073...169362234
%C ...217601...383152...1359050...8146732...11602073...70300633....84490329
%C ..2199713...740408..17630852..11226859..169362234...84490329..1381305433
%C ..1960451..3134584..12757534..66448348..106808569..574957529...742720601
%C .17761659..6273818.142040510..97175595.1363387642..722990905.11158847769
%C .17610501.25715484.117448824.541063232.1001273881.4662288121..7072233273
%H R. H. Hardin, <a href="/A186490/b186490.txt">Table of n, a(n) for n = 1..840</a>
%F Empirical, for every column: a(n)=2*a(n-1)+6*a(n-2)-14*a(n-3)+14*a(n-4)-7*a(n-5) for n>k+13
%e Some solutions for 4X3
%e ..0..5..0....2..6..0....0..0..0....5..0..3....5..1..0....0..0..7....3..1..0
%e ..5..0..5....4..0..6....0..0..0....0..5..0....2..0..1....0..0..0....0..0..1
%e ..0..5..0....0..4..0....4..0..0....1..0..5....0..2..0....7..0..0....0..0..0
%e ..5..0..5....1..0..4....0..4..1....0..1..0....3..0..2....0..7..4....2..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 22 2011
| 