A186486 T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors

1296, 713, 713, 7988, 1638, 7988, 7147, 3343, 3343, 7147, 50755, 13342, 49225, 13342, 50755, 50359, 23790, 36032, 36032, 23790, 50359, 306067, 77358, 306279, 187120, 306279, 77358, 306067, 340221, 146406, 248504, 285899, 285899, 248504, 146406

Offset

1,1

Comments

Table starts

....1296.....713.....7988.....7147....50755.....50359....306067.....340221

.....713....1638.....3343....13342....23790.....77358....146406.....481171

....7988....3343....49225....36032...306279....248504...1851766....1737718

....7147...13342....36032...187120...285899...1112735...1638899....6889391

...50755...23790...306279...285899..2297416...1702449..13845490...11562609

...50359...77358...248504..1112735..1702449...7285701...9428889...45220845

..306067..146406..1851766..1638899.13845490...9428889..85779021...63069609

..340221..481171..1737718..6889391.11562609..45220845..63069609..302363961

.1872721..945714.11287138.10790363.84196426..60712809.524587305..383723349

.2295521.3006488.11961916.42654663.80688693.277373841.440565729.1871999205

Links

R. H. Hardin, Table of n, a(n) for n = 1..967

Formula

Empirical, for every column: a(n)=2*a(n-1)+4*a(n-2)-10*a(n-3)+10*a(n-4)-5*a(n-5) for n>k+13

Example

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

Crossrefs

Sequence in context: A043392 A179536 A273631 * A186485 A281399 A043372

Adjacent sequences: A186483 A186484 A186485 * A186487 A186488 A186489

Keyword

nonn,tabl

Author

R. H. Hardin Feb 22 2011

Status

approved