A186490 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

4096, 1709, 1709, 33182, 4834, 33182, 23215, 9789, 9789, 23215, 275175, 49867, 269126, 49867, 275175, 217601, 91096, 144828, 144828, 91096, 217601, 2199713, 383152, 2196353, 1024481, 2196353, 383152, 2199713, 1960451, 740408, 1359050

Offset

1,1

Comments

Table starts

.....4096.....1709.....33182.....23215.....275175.....217601.....2199713

.....1709.....4834......9789.....49867......91096.....383152......740408

....33182.....9789....269126....144828....2196353....1359050....17630852

....23215....49867....144828...1024481....1510299....8146732....11226859

...275175....91096...2196353...1510299...21122896...11602073...169362234

...217601...383152...1359050...8146732...11602073...70300633....84490329

..2199713...740408..17630852..11226859..169362234...84490329..1381305433

..1960451..3134584..12757534..66448348..106808569..574957529...742720601

.17761659..6273818.142040510..97175595.1363387642..722990905.11158847769

.17610501.25715484.117448824.541063232.1001273881.4662288121..7072233273

Links

R. H. Hardin, Table of n, a(n) for n = 1..840

Formula

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

Example

Some solutions for 4X3
..0..5..0....2..6..0....0..0..0....5..0..3....5..1..0....0..0..7....3..1..0
..5..0..5....4..0..6....0..0..0....0..5..0....2..0..1....0..0..0....0..0..1
..0..5..0....0..4..0....4..0..0....1..0..5....0..2..0....7..0..0....0..0..0
..5..0..5....1..0..4....0..4..1....0..1..0....3..0..2....0..7..4....2..0..0

Crossrefs

Sequence in context: A369823 A176768 A223601 * A223694 A186489 A221261

Adjacent sequences: A186487 A186488 A186489 * A186491 A186492 A186493

Keyword

nonn,tabl

Author

R. H. Hardin Feb 22 2011

Status

approved