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%I #4 Jan 22 2016 08:00:11
%S 1,2,2,4,14,5,11,96,122,13,29,726,2304,938,34,77,5046,47916,43972,
%T 6734,88,201,35574,878004,2331981,754852,45938,225,525,242406,
%U 16435188,104491831,98614986,12017350,302402,569,1361,1653750,292341636
%N T(n,k)=Number of nXk 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
%C Table starts
%C ....1........2............4..............11...............29................77
%C ....2.......14...........96.............726.............5046.............35574
%C ....5......122.........2304...........47916...........878004..........16435188
%C ...13......938........43972.........2331981........104491831........4817531571
%C ...34.....6734.......754852........98614986......10441322974.....1145682971200
%C ...88....45938.....12017350......3774659262.....922017784240...235078226435316
%C ..225...302402....181535822....134786758099...74691010105571.43513012231778789
%C ..569..1939154...2638824216...4574297266940.5680483902454184
%C .1426.12192302..37263580006.149403639631334
%C .3548.75508538.514648921140
%H R. H. Hardin, <a href="/A267911/b267911.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = 5*a(n-1) -7*a(n-2) +a(n-3) +2*a(n-4)
%F k=2: a(n) = 14*a(n-1) -60*a(n-2) +50*a(n-3) +145*a(n-4) -80*a(n-5) -84*a(n-6) +16*a(n-7)
%F k=3: [order 54]
%F Empirical for row n:
%F n=1: a(n) = 3*a(n-1) +2*a(n-2) -8*a(n-3) for n>5
%F n=2: [order 6] for n>8
%F n=3: [order 10] for n>12
%e Some solutions for n=3 k=4
%e ..0..1..2..2....0..1..1..0....0..1..1..0....0..1..1..0....0..1..2..1
%e ..1..2..0..0....1..2..2..1....0..2..1..2....2..2..1..1....2..0..2..0
%e ..1..1..2..1....2..2..1..1....2..0..1..0....2..1..1..0....2..1..0..0
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 22 2016
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