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%I #4 May 15 2014 19:20:32
%S 3,4,5,4,11,8,4,12,30,13,4,12,40,82,21,4,12,41,143,224,34,4,12,41,158,
%T 528,612,55,4,12,41,159,663,1979,1672,89,4,12,41,159,684,2944,7466,
%U 4568,144,4,12,41,159,685,3204,13537,28246,12480,233,4,12,41,159,685,3232
%N T(n,k)=Number of length n+2 0..k arrays with no three equal elements in a row and new values 0..k introduced in 0..k order
%C Table starts
%C ...3.....4......4.......4.......4.......4.......4.......4.......4.......4
%C ...5....11.....12......12......12......12......12......12......12......12
%C ...8....30.....40......41......41......41......41......41......41......41
%C ..13....82....143.....158.....159.....159.....159.....159.....159.....159
%C ..21...224....528.....663.....684.....685.....685.....685.....685.....685
%C ..34...612...1979....2944....3204....3232....3233....3233....3233....3233
%C ..55..1672...7466...13537...16042...16497...16533...16534...16534...16534
%C ..89..4568..28246...63551...84412...90075...90817...90862...90863...90863
%C .144.12480.106992..301968..460174..520248..531812..532958..533013..533014
%C .233.34096.405481.1444795.2570411.3143900.3295779.3317613.3319308.3319374
%H R. H. Hardin, <a href="/A242472/b242472.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) +2*a(n-2)
%F k=3: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)
%F k=4: a(n) = 7*a(n-1) -7*a(n-2) -20*a(n-3) +10*a(n-4) +24*a(n-5) +8*a(n-6)
%F k=5: [order 8]
%F k=6: [order 10]
%F k=7: [order 12]
%F k=8: [order 14]
%e Some solutions for n=4 k=4
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....1....1....1....1....1....0....1....1....1....1....1....1....1....1....0
%e ..0....2....2....1....1....0....1....2....2....2....1....1....2....2....2....1
%e ..1....2....3....2....2....2....2....0....1....3....2....0....3....3....3....0
%e ..2....3....3....3....3....3....3....1....3....1....1....0....0....3....4....2
%e ..3....0....0....2....4....3....3....0....0....2....1....1....4....2....3....0
%Y Column 1 is A000045(n+3)
%Y Column 2 is A021006(n-1)
%Y Column 3 is A204678(n+2)
%Y Column 4 is A222919(n+2)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, May 15 2014
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