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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 13
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 (list; table; graph; refs; listen; history; text; internal format)
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: A198870 A050457 A195441 * A076891 A071883 A099304

Adjacent sequences:  A239534 A239535 A239536 * A239538 A239539 A239540

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 21 2014

STATUS

approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)