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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
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 21 2014
STATUS
approved