A207149 T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

50, 30, 30, 80, 48, 80, 62, 56, 56, 62, 159, 95, 157, 95, 159, 122, 110, 110, 110, 110, 122, 315, 187, 311, 190, 311, 187, 315, 242, 218, 218, 218, 218, 218, 218, 242, 628, 371, 619, 374, 622, 374, 619, 371, 628, 482, 434, 434, 434, 434, 434, 434, 434, 434, 482, 1254

Offset

1,1

Comments

Table starts

..50..30..80..62..159..122..315..242..628..482.1254...962..2506..1922..5010

..30..48..56..95..110..187..218..371..434..740..866..1478..1730..2954..3458

..80..56.157.110..311..218..619..434.1235..866.2468..1730..4934..3458..9866

..62..95.110.190..218..374..434..742..866.1478.1730..2954..3458..5906..6914

.159.110.311.218..622..434.1238..866.2470.1730.4934..3458..9866..6914.19730

.122.187.218.374..434..754..866.1490.1730.2962.3458..5906..6914.11810.13826

.315.218.619.434.1238..866.2482.1730.4946.3458.9874..6914.19730.13826.39458

.242.371.434.742..866.1490.1730.3010.3458.5954.6914.11842.13826.23618.27650

Links

R. H. Hardin, Table of n, a(n) for n = 1..868

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 8;

k=2: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 9;

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

k=4: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 11;

k=5: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 12;

k=6: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 13;

k=7: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 14;

Apparently a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > k+7.

Example

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

Crossrefs

Sequence in context: A090691 A033980 A342903 * A207142 A244277 A248688

Adjacent sequences: A207146 A207147 A207148 * A207150 A207151 A207152

Keyword

nonn,tabl

Author

R. H. Hardin Feb 15 2012

Status

approved