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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

%I #4 Mar 21 2014 07:11:53

%S 1,2,1,6,2,6,16,6,24,13,44,16,216,68,47,120,44,1536,1014,406,128,328,

%T 120,11616,11108,13254,1584,405,896,328,86400,131988,293741,98304,

%U 7790,1181,2448,896,645504,1533792,7199001,3785280,984150,33630,3598,6688,2448

%N 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

%C Table starts

%C .....1......2.........6...........16..............44...............120

%C .....1......2.........6...........16..............44...............120

%C .....6.....24.......216.........1536...........11616.............86400

%C ....13.....68......1014........11108..........131988...........1533792

%C ....47....406.....13254.......293741.........7199001.........171712936

%C ...128...1584.....98304......3785280.......165336096........6976042240

%C ...405...7790....984150.....71388971......5988724293......482858009716

%C ..1181..33630...8368566...1093269814....169350916116....25030781490504

%C ..3598.156032..77673624..18727824939...5466853947751..1514104924173186

%C .10705.695344.687582150.301846514891.164296850179323.84271877225127052

%H R. H. Hardin, <a href="/A239537/b239537.txt">Table of n, a(n) for n = 1..128</a>

%F Empirical for column k:

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

%F k=2: [order 10]

%F 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)

%F Empirical for row n:

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

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

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

%F n=4: [order 10]

%F n=5: [order 37]

%F n=6: [order 85]

%e Some solutions for n=4 k=4

%e ..0..1..0..0..1....0..1..2..1..2....0..1..1..2..1....0..1..2..0..2

%e ..0..1..0..0..1....0..1..2..1..2....0..1..1..2..1....0..1..2..0..2

%e ..0..2..0..2..1....1..2..2..1..2....0..1..1..0..1....0..1..2..0..2

%e ..0..2..0..2..1....1..2..2..1..0....2..0..2..0..2....1..0..2..1..2

%e ..0..2..0..2..1....1..2..2..1..0....2..0..2..0..2....1..0..2..1..2

%Y Row 1 and 2 are A002605

%Y Row 3 is A231317

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Mar 21 2014

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)