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

Author

R. H. Hardin, Mar 21 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Row 1 and 2 are A002605

Row 3 is A231317

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]