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%I #10 Aug 18 2017 18:10:49
%S 10,359,4064,25206,108250,363349,1022672,2522796,5618202,11530915,
%T 22141328,40225250,69742218,116180113,186961120,291914072,443818218,
%U 659023455,958152064,1366886990,1916851706,2646586701,3602627632
%N Number of length 3+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 3 of A249844.
%H R. H. Hardin, <a href="/A249847/b249847.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^7 + (6/5)*n^6 + 3*n^5 + 3*n^4 + (5/6)*n^3 + (4/5)*n^2 + (1/6)*n.
%F Conjectures from _Colin Barker_, Aug 18 2017: (Start)
%F G.f.: x*(10 + 279*x + 1472*x^2 + 2186*x^3 + 990*x^4 + 103*x^5) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F (End)
%e Some solutions for n=5
%e ..0....1....4....3....1....0....5....1....1....5....5....0....5....4....2....5
%e ..4....5....0....2....4....0....0....2....2....1....3....0....2....4....3....2
%e ..5....1....3....0....0....2....5....4....3....0....0....3....4....0....0....1
%e ..3....4....2....0....0....1....2....1....0....4....4....3....1....0....3....5
%e ..2....2....3....3....2....4....4....4....2....0....2....2....3....2....1....4
%e ..1....1....0....5....4....0....0....5....1....2....0....3....4....2....4....0
%e ..1....2....0....4....2....5....0....3....5....4....5....0....2....3....4....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 07 2014
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