A232459 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally, vertically, diagonally or antidiagonally

1, 3, 3, 7, 51, 7, 15, 381, 381, 15, 33, 3015, 8227, 3015, 33, 73, 24651, 187989, 187989, 24651, 73, 161, 198945, 4423815, 12521603, 4423815, 198945, 161, 355, 1607067, 103104905, 865692227, 865692227, 103104905, 1607067, 355, 783, 12991131

Offset

1,2

Comments

Table starts

...1.......3..........7............15...............33...................73

...3......51........381..........3015............24651...............198945

...7.....381.......8227........187989..........4423815............103104905

..15....3015.....187989......12521603........865692227..........59192688269

..33...24651....4423815.....865692227.....176788379233.......35630507175345

..73..198945..103104905...59192688269...35630507175345....21136983701111465

.161.1607067.2403848151.4047993038079.7183387830867849.12543745301001506913

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) +12*a(n-2) +39*a(n-3)

k=3: [order 9]

k=4: [order 15]

k=5: [order 46]

Example

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

Crossrefs

Column 1 is A193641

Sequence in context: A232309 A273043 A066142 * A175566 A349425 A248859

Adjacent sequences: A232456 A232457 A232458 * A232460 A232461 A232462

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 24 2013

Status

approved