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A250157 Number of length 3+6 0..n arrays with every seven consecutive terms having the maximum of some two terms equal to the minimum of the remaining five terms. 1

%I #8 Nov 12 2018 14:36:13

%S 354,8377,79740,455055,1879526,6219899,17519352,43657365,98808010,

%T 206916501,406440244,756627027,1345629390,2300780615,3801384176,

%U 6094394889,9513396402,14501306065,21637264620,31668194551,45545537334

%N Number of length 3+6 0..n arrays with every seven consecutive terms having the maximum of some two terms equal to the minimum of the remaining five terms.

%H R. H. Hardin, <a href="/A250157/b250157.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (55/84)*n^8 + (67/7)*n^7 + (151/4)*n^6 + 70*n^5 + (1061/12)*n^4 + (521/6)*n^3 + (1377/28)*n^2 + (445/42)*n + 1.

%F Conjectures from _Colin Barker_, Nov 12 2018: (Start)

%F G.f.: x*(354 + 5191*x + 17091*x^2 + 9231*x^3 - 4393*x^4 - 1117*x^5 + 51*x^6 - 9*x^7 + x^8) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

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

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

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

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

%Y Row 3 of A250154.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2014

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