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%I #4 Jun 08 2014 08:44:53
%S 4,4,8,4,9,16,4,9,21,32,4,9,21,50,64,4,9,21,51,120,128,4,9,21,51,127,
%T 289,256,4,9,21,51,127,323,697,512,4,9,21,51,127,324,835,1682,1024,4,
%U 9,21,51,127,324,844,2187,4060,2048,4,9,21,51,127,324,844,2242,5787,9801,4096,4
%N T(n,k)=Number of length n+2 0..k arrays with no three unequal elements in a row and new values 0..k introduced in 0..k order
%C Table starts
%C ....4....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4
%C ....8....9.....9.....9.....9.....9.....9.....9.....9.....9.....9.....9.....9
%C ...16...21....21....21....21....21....21....21....21....21....21....21....21
%C ...32...50....51....51....51....51....51....51....51....51....51....51....51
%C ...64..120...127...127...127...127...127...127...127...127...127...127...127
%C ..128..289...323...324...324...324...324...324...324...324...324...324...324
%C ..256..697...835...844...844...844...844...844...844...844...844...844...844
%C ..512.1682..2187..2242..2243..2243..2243..2243..2243..2243..2243..2243..2243
%C .1024.4060..5787..6062..6073..6073..6073..6073..6073..6073..6073..6073..6073
%C .2048.9801.15435.16655.16736.16737.16737.16737.16737.16737.16737.16737.16737
%H R. H. Hardin, <a href="/A243641/b243641.txt">Table of n, a(n) for n = 1..9999</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) -a(n-2) -a(n-3)
%F k=3: a(n) = 5*a(n-1) -6*a(n-2) -2*a(n-3) +4*a(n-4)
%F k=4: a(n) = 7*a(n-1) -14*a(n-2) +21*a(n-4) -7*a(n-5) -6*a(n-6)
%F k=5: [order 8]
%F k=6: [order 10]
%F k=7: [order 12]
%F k=8: [order 14]
%F k=9: [order 16]
%e Some solutions for n=6 k=4
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....0....0....0....1....1....0....0....0....0....1....1....0....1....1....0
%e ..1....1....1....0....1....0....0....0....1....1....1....0....0....1....1....1
%e ..1....1....0....1....1....0....1....0....0....1....2....0....1....2....2....1
%e ..2....2....0....0....0....0....0....0....0....2....1....1....1....2....2....0
%e ..2....1....1....1....1....1....0....0....0....1....1....1....0....1....3....1
%e ..3....1....1....1....0....0....0....0....1....1....1....1....0....1....3....1
%e ..2....2....1....1....1....1....0....1....1....1....0....0....2....2....0....0
%Y Column 1 is A000079(n+1)
%Y Column 2 is A024537(n+1)
%Y Column 3 is A094286(n+2)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jun 08 2014