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%I #4 Mar 07 2014 07:23:49
%S 12,116,36,782,864,144,5008,13090,13456,540,34302,191086,611524,
%T 176224,2052,238418,3025468,25080064,22636472,2391340,7776,1646042,
%U 48511734,1176627204,2531484558,873385842,32225410,29484,11326068,773430790
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors
%C Table starts
%C .....12........116............782...............5008..................34302
%C .....36........864..........13090.............191086................3025468
%C ....144......13456.........611524...........25080064.............1176627204
%C ....540.....176224.......22636472.........2531484558...........330899764092
%C ...2052....2391340......873385842.......265992385206.........98434762200590
%C ...7776...32225410....33476445936.....27816714540010......29028870095730324
%C ..29484..434883190..1285018853980...2912187511240098....8576772023696061986
%C .111780.5866480970.49292627209040.304661966072695432.2532114793289297959122
%H R. H. Hardin, <a href="/A238929/b238929.txt">Table of n, a(n) for n = 1..83</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) +3*a(n-2)
%F k=2: [order 29]
%F Empirical for row n:
%F n=1: [linear recurrence of order 18]
%e Some solutions for n=2 k=4
%e ..1..2..2..2..1....0..0..1..1..0....0..0..0..3..3....0..0..2..3..3
%e ..3..3..1..0..0....2..2..2..3..3....1..1..2..2..1....2..2..0..0..0
%e ..1..2..2..3..3....0..1..1..0..0....0..3..3..3..0....0..1..3..3..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 07 2014