A206343 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor

192, 96, 96, 455, 181, 455, 296, 232, 232, 296, 1376, 534, 1340, 534, 1376, 880, 686, 682, 682, 686, 880, 4111, 1589, 4007, 1581, 4007, 1589, 4111, 2622, 2042, 2030, 2034, 2034, 2030, 2042, 2622, 12319, 4751, 12005, 4711, 12021, 4711, 12005, 4751, 12319

Offset

1,1

Comments

Table starts

..192...96...455...296..1376...880...4111...2622..12319...7854..36945...23550

...96..181...232...534...686..1589...2042...4751...6110..14239..18318...42705

..455..232..1340...682..4007..2030..12005...6074..35999..18206.107983...54606

..296..534...682..1581..2034..4711...6078..14101..18210..42271..54606..126799

.1376..686..4007..2034.12021..6090..36015..18222.107997..54618.323943..163806

..880.1589..2030..4711..6090.14181..18258..42351..54654.126861.163842..380391

.4111.2042.12005..6078.36015.18258.108141..54762.324087.163950.971925..491514

.2622.4751..6074.14101.18222.42351..54762.127581.164274.381111.491838.1141701

Links

R. H. Hardin, Table of n, a(n) for n = 1..2380

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>10

k=2: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>11

k=3: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>12

k=4: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>13

k=5: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>14

k=6: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>15

k=7: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>16

apparently a(n-1)+3*a(n-2)-3*a(n-3) for n>k+9

Example

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

Crossrefs

Sequence in context: A155843 A187527 A187698 * A206336 A206335 A289219

Adjacent sequences: A206340 A206341 A206342 * A206344 A206345 A206346

Keyword

nonn,tabl

Author

R. H. Hardin Feb 06 2012

Status

approved