A190023 T(n,m)=Number of (n+1)X3 0..m arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors

21, 83, 30, 205, 129, 51, 419, 362, 243, 88, 713, 839, 701, 562, 128, 1169, 1638, 1715, 2049, 903, 197, 1709, 2923, 3343, 5879, 3442, 1754, 292, 2471, 4834, 5947, 13342, 10259, 8223, 2937, 457, 3381, 7605, 9789, 26982, 23790, 28628, 14492, 5790, 688

Offset

1,1

Comments

Table starts

...21....83....205....419.....713....1169.....1709.....2471......3381......4543

...30...129....362....839....1638....2923.....4834.....7605.....11434.....16493

...51...243....701...1715....3343....5947.....9789....15499.....23561.....33877

...88...562...2049...5879...13342...26982....49867....87001....143918....224458

..128...903...3442..10259...23790...48875....91096...160377....267770....420837

..197..1754...8223..28628...77358..181792...383152...749237...1371936...2357920

..292..2937..14492..53045..146406..349085...740408..1460393...2698956...4662219

..457..5790..35081.150208..481171.1308972..3134584..6868867..13933702..26279979

..688..9993..64280.289063..945714.2606517..6273818.13842067..28288458..53533915

.1058.19236.150785.792360.3006488.9456818.25715484.63104546.141749332.293291390

Links

R. H. Hardin, Table of n, a(n) for n = 1..2450

Formula

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>(7+2*A072649(m)), except for n>8 for m=1.

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

Example

Some solutions for n=4 m=4
..3..0..0....0..4..0....3..3..3....3..3..0....0..1..3....2..3..0....4..2..0
..3..0..0....3..0..4....0..0..0....0..0..3....0..0..1....0..0..3....3..0..2
..0..3..0....0..3..0....0..0..0....0..0..0....0..0..0....0..0..0....0..3..0
..2..0..3....1..0..3....3..0..0....0..0..0....1..0..0....2..0..0....3..0..3
..0..2..4....0..1..0....4..3..0....2..2..2....4..1..0....0..2..1....0..3..1

Crossrefs

Sequence in context: A219593 A195961 A359024 * A071397 A064762 A104676

Adjacent sequences: A190020 A190021 A190022 * A190024 A190025 A190026

Keyword

nonn,tabl

Author

R. H. Hardin May 04 2011

Status

approved