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%I #8 Nov 12 2018 05:26:54
%S 107,1452,9160,37805,119391,313852,722072,1501425,2883835,5196356,
%T 8884272,14536717,22914815,34982340,51938896,75255617,106713387,
%U 148443580,202971320,273261261,362765887,475476332,615975720,789495025
%N Number of length 1+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="/A250155/b250155.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (7/2)*n^6 + 14*n^5 + (105/4)*n^4 + (63/2)*n^3 + (91/4)*n^2 + 8*n + 1.
%F Conjectures from _Colin Barker_, Nov 12 2018: (Start)
%F G.f.: x*(107 + 703*x + 1243*x^2 + 432*x^3 + 41*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=5:
%e ..0....3....2....3....4....2....4....0....4....0....3....3....3....3....0....1
%e ..3....1....4....4....4....3....0....3....2....0....2....5....1....4....4....5
%e ..0....2....2....5....2....0....5....2....2....5....1....5....4....0....1....4
%e ..3....0....3....4....2....4....0....3....3....0....1....5....2....2....1....3
%e ..4....0....0....5....3....0....0....2....0....5....0....4....3....3....3....0
%e ..0....1....5....4....5....0....4....5....2....4....1....5....4....5....3....1
%e ..0....0....5....5....0....3....3....5....5....2....5....4....2....2....3....5
%Y Row 1 of A250154.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 13 2014
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