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A267911 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.

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