A250085 - OEIS

%I #11 Nov 12 2018 03:00:27

%S 252,5084,42936,222329,847708,2623376,6978064,16547001,35852668,

%T 72229740,137044040,247259649,427412636,712054192,1148730272,

%U 1801569169,2755552764,4121551516,6042207576,8698754729,12318868188,17185641584

%N Number of length 4+5 0..n arrays with every six consecutive terms having the maximum of some two terms equal to the minimum of the remaining four terms.

%H R. H. Hardin, <a href="/A250085/b250085.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (3/28)*n^8 + (121/35)*n^7 + (85/4)*n^6 + (501/10)*n^5 + (249/4)*n^4 + (1717/30)*n^3 + (1159/28)*n^2 + (1597/105)*n + 1.

%F Conjectures from _Colin Barker_, Nov 11 2018: (Start)

%F G.f.: x*(252 + 2816*x + 6252*x^2 - 2239*x^3 - 2861*x^4 + 56*x^5 + 52*x^6 - 9*x^7 + x^8) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=3:

%e   3  2  2  0  2  2  3  3  3  2  1  0  1  0  3  1

%e   0  0  2  2  0  3  3  3  3  2  0  3  1  2  3  1

%e   2  1  1  2  0  0  3  2  1  0  0  3  3  2  2  1

%e   3  0  1  0  2  1  0  0  1  3  2  2  1  0  1  1

%e   2  0  0  0  0  1  0  0  3  2  2  0  1  0  1  3

%e   2  1  2  0  0  2  0  0  1  2  0  0  2  0  1  3

%e   2  0  1  1  0  2  2  0  1  2  1  0  1  3  3  0

%e   3  2  1  3  0  2  1  0  1  2  0  3  2  3  2  1

%e   0  1  3  1  1  0  0  3  1  2  0  3  3  0  0  3

%Y Row 4 of A250081.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 11 2014