%I #11 Aug 22 2017 06:35:59
%S 21,7054,348066,6415638,65419155,449532868,2330996068,9790907652,
%T 34925259201,109359675810,307898807590,793597679082,1898570817663,
%U 4261710821064,9053571280840,18330419662312,35574363778221
%N Number of length 5+6 0..n arrays with no seven consecutive terms having the maximum of any two terms equal to the minimum of the remaining five terms.
%C Row 5 of A250059.
%H R. H. Hardin, <a href="/A250063/b250063.txt">Table of n, a(n) for n = 1..41</a>
%F Empirical: a(n) = n^11 + (107/420)*n^10 + (9701/1512)*n^9 + (117/28)*n^8 - (919/252)*n^7 + (2677/180)*n^6 - (109/72)*n^5 - (421/63)*n^4 + (6647/756)*n^3 - (535/252)*n^2 - (23/42)*n.
%F Conjectures from _Colin Barker_, Aug 22 2017: (Start)
%F G.f.: x*(21 + 6802*x + 264804*x^2 + 2699790*x^3 + 9862370*x^4 + 14835694*x^5 + 9550828*x^6 + 2483826*x^7 + 209945*x^8 + 2720*x^9) / (1 - x)^12.
%F a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12.
%F (End)
%e Some solutions for n=2:
%e ..0....2....0....2....0....2....2....2....1....1....2....0....0....1....0....1
%e ..2....1....1....2....1....1....2....2....0....1....2....2....2....1....2....2
%e ..2....0....1....2....1....2....1....2....2....0....2....2....1....1....1....2
%e ..2....2....2....2....2....1....2....1....2....2....2....2....2....0....2....1
%e ..1....2....2....0....0....0....0....2....2....0....0....2....1....2....0....0
%e ..0....2....0....2....1....2....0....0....0....1....2....2....0....2....2....2
%e ..2....0....2....1....2....0....2....2....1....2....1....0....2....0....2....0
%e ..2....2....0....0....0....1....2....0....2....2....0....1....0....2....0....1
%e ..2....1....1....2....2....1....1....2....0....2....2....2....2....1....2....1
%e ..0....0....2....2....1....2....1....2....2....0....1....0....2....1....1....2
%e ..1....1....1....1....2....1....1....2....2....2....2....1....2....0....2....2
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 11 2014