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%I #10 Aug 20 2017 23:30:15
%S 6,966,26578,309452,2160160,10755158,42158796,138336744,395723154,
%T 1015071750,2382851790,5197343476,10655843900,20723014006,38504379320,
%U 68753342352,118544772606,198153311046,322179959658,510976323420
%N Number of length 6+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 6 of A250387.
%H R. H. Hardin, <a href="/A250392/b250392.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^9 - (7/30)*n^8 + (1229/315)*n^7 - (23/30)*n^6 + (49/36)*n^5 + (67/30)*n^4 - (493/180)*n^3 + (53/30)*n^2 - (11/21)*n.
%F Conjectures from _Colin Barker_, Aug 20 2017: (Start)
%F G.f.: 2*x*(3 + 453*x + 8594*x^2 + 43211*x^3 + 73495*x^4 + 45443*x^5 + 9692*x^6 + 549*x^7) / (1 - x)^10.
%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
%F (End)
%e Some solutions for n=3:
%e ..0....2....2....1....0....2....2....0....3....0....1....0....0....0....2....1
%e ..2....3....0....3....1....0....0....2....0....1....0....3....1....0....0....3
%e ..3....3....2....3....0....1....0....1....3....0....0....2....3....3....2....3
%e ..0....2....1....2....2....3....3....3....0....2....2....0....2....2....0....2
%e ..1....1....0....0....3....2....1....0....2....3....3....1....0....0....3....0
%e ..3....3....0....3....1....3....2....0....1....0....3....3....3....1....3....3
%e ..3....3....3....0....0....1....0....2....2....1....0....2....3....2....2....1
%e ..0....0....1....3....0....3....3....1....1....0....0....3....0....0....0....3
%e ..0....1....0....0....2....0....0....3....3....1....2....2....1....2....0....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 20 2014