A239537 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order

1, 2, 1, 6, 2, 6, 16, 6, 24, 13, 44, 16, 216, 68, 47, 120, 44, 1536, 1014, 406, 128, 328, 120, 11616, 11108, 13254, 1584, 405, 896, 328, 86400, 131988, 293741, 98304, 7790, 1181, 2448, 896, 645504, 1533792, 7199001, 3785280, 984150, 33630, 3598, 6688, 2448

Offset

1,2

Comments

Table starts

.....1......2.........6...........16..............44...............120

.....1......2.........6...........16..............44...............120

.....6.....24.......216.........1536...........11616.............86400

....13.....68......1014........11108..........131988...........1533792

....47....406.....13254.......293741.........7199001.........171712936

...128...1584.....98304......3785280.......165336096........6976042240

...405...7790....984150.....71388971......5988724293......482858009716

..1181..33630...8368566...1093269814....169350916116....25030781490504

..3598.156032..77673624..18727824939...5466853947751..1514104924173186

.10705.695344.687582150.301846514891.164296850179323.84271877225127052

Links

R. H. Hardin, Table of n, a(n) for n = 1..128

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +4*a(n-2) -3*a(n-3)

k=2: [order 10]

k=3: a(n) = 8*a(n-1) +26*a(n-2) -166*a(n-3) +96*a(n-4) +198*a(n-5) -81*a(n-6)

Empirical for row n:

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

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

n=3: a(n) = 6*a(n-1) +12*a(n-2) -8*a(n-3)

n=4: [order 10]

n=5: [order 37]

n=6: [order 85]

Example

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

Crossrefs

Row 1 and 2 are A002605

Row 3 is A231317

Sequence in context: A050457 A195441 A338025 * A076891 A071883 A368241

Adjacent sequences: A239534 A239535 A239536 * A239538 A239539 A239540

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 21 2014

Status

approved