%I #8 Aug 18 2017 18:10:39

%S 10,198,1500,6916,23526,65226,156184,335016,659682,1213102,2109492,

%T 3501420,5587582,8621298,12919728,18873808,26958906,37746198,51914764,

%U 70264404,93729174,123391642,160497864,206473080,262938130,331726590

%N Number of length 2+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 2 of A249844.

%H R. H. Hardin, <a href="/A249846/b249846.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + (9/5)*n^5 + 3*n^4 + 3*n^3 + n^2 + (1/5)*n.

%F Conjectures from _Colin Barker_, Aug 18 2017: (Start)

%F G.f.: 2*x*(5 + 64*x + 162*x^2 + 112*x^3 + 17*x^4) / (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=6

%e ..4....5....1....0....5....0....1....6....5....3....6....5....0....5....1....5

%e ..6....1....0....1....6....1....6....0....0....1....1....0....5....3....2....4

%e ..5....3....4....0....3....5....3....3....2....5....6....4....2....5....0....1

%e ..6....5....0....6....0....3....4....3....0....6....6....0....4....4....5....4

%e ..6....0....1....4....0....0....2....0....2....5....2....4....1....3....3....2

%e ..4....3....5....3....4....2....4....5....1....3....0....4....0....5....4....4

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2014