A207050 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X3 or 3X2 subblock having exactly one clockwise edge increases

81, 150, 150, 441, 270, 441, 1416, 552, 552, 1416, 4371, 1182, 750, 1182, 4371, 13386, 2244, 1272, 1272, 2244, 13386, 41589, 4722, 2094, 2244, 2094, 4722, 41589, 128700, 9582, 3408, 3408, 3408, 3408, 9582, 128700, 397335, 18930, 5850, 4836, 4944, 4836

Offset

1,1

Comments

Table starts

.....81...150..441..1416..4371.13386.41589.128700.397335.1229310.3802377

....150...270..552..1182..2244..4722..9582..18930..39348...78804..159042

....441...552..750..1272..2094..3408..5850...9792..15966...26880...45024

...1416..1182.1272..2244..3408..4836..9144..13950..19752...36912...55944

...4371..2244.2094..3408..4944..7584.13752..20208..31158...55920...81936

..13386..4722.3408..4836..7584.11712.19200..30528..48096...78744..125184

..41589..9582.5850..9144.13752.19200.35904..54528..77376..146304..223200

.128700.18930.9792.13950.20208.30528.54528..79104.121344..220032..323328

Links

R. H. Hardin, Table of n, a(n) for n = 1..1624

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +a(n-2) +8*a(n-3) -2*a(n-4) for n>5

k=2: a(n) = 2*a(n-2) +5*a(n-3) -a(n-4) -a(n-5) for n>7

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

k=4: a(n) = 4*a(n-3) for n>12

k=5: a(n) = 4*a(n-3) for n>13

k=6: a(n) = 4*a(n-3) for n>14

k=7: a(n) = 4*a(n-3) for n>15

apparently a(n) = 4*a(n-3) for k>3 and n>k+8

Example

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

Crossrefs

Sequence in context: A046374 A153259 A369977 * A206072 A207043 A206065

Adjacent sequences: A207047 A207048 A207049 * A207051 A207052 A207053

Keyword

nonn,tabl

Author

R. H. Hardin Feb 14 2012

Status

approved