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%I #11 Aug 20 2017 23:30:08
%S 6,78,432,1560,4350,10206,21168,40032,70470,117150,185856,283608,
%T 418782,601230,842400,1155456,1555398,2059182,2685840,3456600,4395006,
%U 5527038,6881232,8488800,10383750,12603006,15186528,18177432,21622110,25570350
%N Number of length 2+3 0..n arrays with no four consecutive terms having the maximum of any two terms equal to the minimum of the remaining two terms.
%C Row 2 of A250387.
%H R. H. Hardin, <a href="/A250388/b250388.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^5 + (3/2)*n^4 + 2*n^3 + (3/2)*n^2.
%F Conjectures from _Colin Barker_, Aug 20 2017: (Start)
%F G.f.: 6*x*(1 + x)*(1 + 6*x + 3*x^2) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F (End)
%e Some solutions for n=6:
%e ..5....4....1....3....2....1....1....6....6....1....5....1....0....2....6....4
%e ..3....6....2....0....5....2....0....6....4....5....6....0....5....2....2....6
%e ..1....2....3....5....6....6....6....1....1....0....6....6....5....5....4....5
%e ..1....0....4....5....0....5....6....2....0....6....0....4....1....4....3....1
%e ..5....1....5....0....1....0....5....6....0....3....3....3....4....5....1....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 20 2014
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