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Number of length 6+4 0..n arrays with no five consecutive terms having the maximum of any two terms equal to the minimum of the remaining three terms.
1

%I #8 Aug 18 2017 18:11:13

%S 10,2163,81816,1234328,10653298,63374127,289372688,1084868616,

%T 3492375066,9959590531,25736172264,61283393808,136218299906,

%U 285494859439,568743409824,1083950013296,1986962835498,3518666938611,6042075583672

%N Number of length 6+4 0..n arrays with no five consecutive terms having the maximum of any two terms equal to the minimum of the remaining three terms.

%C Row 6 of A249844.

%H R. H. Hardin, <a href="/A249850/b249850.txt">Table of n, a(n) for n = 1..152</a>

%F Empirical: a(n) = n^10 - (19/35)*n^9 + (4327/840)*n^8 - (104/63)*n^7 + (52/15)*n^6 + (367/90)*n^5 - (491/120)*n^4 + (389/126)*n^3 - (221/420)*n^2 + (1/35)*n.

%F Conjectures from _Colin Barker_, Aug 18 2017: (Start)

%F G.f.: x*(10 + 2053*x + 58573*x^2 + 451667*x^3 + 1221975*x^4 + 1285419*x^5 + 529155*x^6 + 77117*x^7 + 2831*x^8) / (1 - x)^11.

%F a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

%F (End)

%e Some solutions for n=3

%e ..0....0....1....0....0....1....2....3....3....2....2....2....0....1....3....1

%e ..0....2....3....2....2....3....3....0....2....2....3....0....0....3....1....2

%e ..3....3....0....2....1....3....3....3....3....3....3....3....3....2....2....0

%e ..3....0....3....1....3....0....0....3....1....1....0....3....1....0....0....0

%e ..3....1....0....2....3....3....0....0....0....0....1....0....3....0....0....3

%e ..0....3....3....0....3....1....3....2....0....0....3....2....2....2....1....2

%e ..2....2....1....3....0....3....1....1....3....1....0....0....1....3....2....1

%e ..1....3....2....2....2....0....2....3....3....3....2....3....2....2....2....0

%e ..0....1....2....0....0....3....0....2....2....2....0....3....0....0....0....0

%e ..2....1....0....1....1....3....0....0....1....2....1....3....0....0....0....1

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2014