A237637 T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with the upper median of every 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.

81, 260, 260, 702, 636, 702, 1786, 1220, 1220, 1786, 4621, 2356, 1310, 2356, 4621, 11936, 4500, 1488, 1488, 4500, 11936, 30656, 8594, 2086, 2012, 2086, 8594, 30656, 77576, 16448, 2900, 2816, 2816, 2900, 16448, 77576, 200452, 31672, 4132, 4440, 4622

Offset

1,1

Comments

Table starts:

.....81....260...702..1786..4621.11936.30656.77576.200452.515424.1325424

....260....636..1220..2356..4500..8594.16448.31672..60362.116180..223768

....702...1220..1310..1488..2086..2900..4132..5720...8248..11504...16546

...1786...2356..1488..2012..2816..4440..5976.10104..14168..22294...29908

...4621...4500..2086..2816..4622..5656..7756.11312..17626..22624...30496

..11936...8594..2900..4440..5656..9368.11984.20756..28336..47134...59920

..30656..16448..4132..5976..7756.11984.18344.23968..35732..47936...71426

..77576..31672..5720.10104.11312.20756.23968.44292..56672..98684..119840

.200452..60362..8248.14168.17626.28336.35732.56672.102536.113344..166116

.515424.116180.11504.22294.22624.47134.47936.98684.113344.211268..239680

Links

R. H. Hardin, Table of n, a(n) for n = 1..2664

Formula

Empirical for column k:

k=1: a(n) = 36*a(n-4) +48*a(n-6) for n>9.

k=2: a(n) = 3*a(n-3) +10*a(n-4) -12*a(n-7) -6*a(n-8) for n>12.

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

k=4: a(n) = 5*a(n-4) for n>14.

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

k=6: a(n) = 5*a(n-4) for n>14.

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

diagonal: a(n) = 4*a(n-2) +25*a(n-4) -100*a(n-6) for n>11.

Example

Some solutions for n=5, k=4:
..1..1..0..1..2....0..0..0..1..2....2..1..0..2..1....2..1..0..1..2
..0..0..0..2..1....2..1..0..1..2....0..2..0..0..0....0..0..0..2..1
..0..1..2..1..0....1..2..0..0..0....0..1..2..1..0....0..1..2..1..0
..1..2..0..0..0....0..0..2..1..0....0..0..0..2..1....0..2..0..0..0
..2..1..0..1..2....1..0..1..2..0....1..2..0..1..2....2..1..0..1..2
..1..0..0..2..1....1..0..0..1..2....2..1..0..0..1....1..0..0..2..0

Crossrefs

Sequence in context: A237060 A361179 A340697 * A237630 A236746 A236739

Adjacent sequences: A237634 A237635 A237636 * A237638 A237639 A237640

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 10 2014

Status

approved