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%I #4 Jun 09 2014 11:07:43
%S 3,3,5,3,6,8,3,6,12,13,3,6,12,24,21,3,6,12,25,48,34,3,6,12,25,53,96,
%T 55,3,6,12,25,53,115,192,89,3,6,12,25,53,116,253,384,144,3,6,12,25,53,
%U 116,259,564,768,233,3,6,12,25,53,116,259,593,1268,1536,377,3,6,12,25,53,116,259
%N T(n,k)=Number of length n+2 0..k arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..k introduced in 0..k order
%C Table starts
%C ...3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3
%C ...5....6....6....6....6....6....6....6....6....6....6....6....6....6....6....6
%C ...8...12...12...12...12...12...12...12...12...12...12...12...12...12...12...12
%C ..13...24...25...25...25...25...25...25...25...25...25...25...25...25...25...25
%C ..21...48...53...53...53...53...53...53...53...53...53...53...53...53...53...53
%C ..34...96..115..116..116..116..116..116..116..116..116..116..116..116..116..116
%C ..55..192..253..259..259..259..259..259..259..259..259..259..259..259..259..259
%C ..89..384..564..593..594..594..594..594..594..594..594..594..594..594..594..594
%C .144..768.1268.1382.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389
%C .233.1536.2871.3281.3322.3323.3323.3323.3323.3323.3323.3323.3323.3323.3323.3323
%H R. H. Hardin, <a href="/A243729/b243729.txt">Table of n, a(n) for n = 1..9999</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 2*a(n-1)
%F k=3: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -3*a(n-4)
%F k=4: a(n) = 4*a(n-1) -13*a(n-3) +6*a(n-4) +8*a(n-5)
%F k=5: a(n) = 5*a(n-1) -29*a(n-3) +20*a(n-4) +51*a(n-5) -31*a(n-6) -30*a(n-7)
%F k=6: [order 9]
%F k=7: [order 11]
%F k=8: [order 13]
%F k=9: [order 15]
%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 ..0....0....0....0....1....1....1....1....1....1....1....1....1....0....1....0
%e ..1....1....1....1....1....1....0....0....1....1....1....1....0....1....0....1
%e ..1....1....0....0....0....2....1....1....2....2....2....2....0....0....1....1
%e ..0....2....1....1....0....2....0....1....2....2....2....1....2....1....0....0
%e ..0....2....1....0....2....3....1....2....0....3....1....2....2....0....0....1
%e ..1....3....2....1....2....3....1....1....0....2....1....2....3....0....2....1
%e ..0....2....1....1....0....0....0....2....1....3....2....0....3....2....0....2
%Y Column 1 is A000045(n+3)
%Y Column 2 is A003945
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jun 09 2014
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