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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. 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 28 17:22 EST 2022. Contains 358421 sequences. (Running on oeis4.)