A186482 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors

256, 205, 205, 1098, 362, 1098, 1251, 701, 701, 1251, 4895, 2049, 4686, 2049, 4895, 5955, 3442, 4810, 4810, 3442, 5955, 20079, 8223, 20224, 16762, 20224, 8223, 20079, 27101, 14492, 21760, 25633, 25633, 21760, 14492, 27101, 84228, 35081, 82632, 67714

Offset

1,1

Comments

Table starts

....256....205...1098....1251....4895....5955...20079....27101....84228

....205....362....701....2049....3442....8223...14492....35081....64280

...1098....701...4686....4810...20224...21760...82632...101108...344804

...1251...2049...4810...16762...25633...67714..101305...286290...456113

...4895...3442..20224...25633..107353..108025..433513...479785..1793817

...5955...8223..21760...67714..108025..305089..418177..1286113..1812049

..20079..14492..82632..101305..433513..418177.1849873..1894849..7687009

..27101..35081.101108..286290..479785.1286113.1894849..5977657..8078233

..84228..64280.344804..456113.1793817.1812049.7687009..8078233.34498177

.123227.150785.465884.1219034.2226665.5368065.8602033.25049545.36618769

Links

R. H. Hardin, Table of n, a(n) for n = 1..1740

Formula

Empirical, for every column: a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-4)-3*a(n-5) for n>k+11

Example

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

Crossrefs

Sequence in context: A188830 A103949 A057066 * A186474 A093861 A248776

Adjacent sequences: A186479 A186480 A186481 * A186483 A186484 A186485

Keyword

nonn,tabl

Author

R. H. Hardin Feb 22 2011

Status

approved