A250389 - OEIS

%I #8 Aug 21 2017 05:50:38

%S 6,146,1208,5848,20518,58114,141344,306816,609846,1129986,1977272,

%T 3299192,5288374,8190994,12315904,18044480,25841190,36264882,49980792,

%U 67773272,90559238,119402338,155527840,200338240,255429590,322608546

%N Number of length 3+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 3 of A250387.

%H R. H. Hardin, <a href="/A250389/b250389.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + (16/15)*n^5 + (13/6)*n^4 + (5/3)*n^3 - (1/6)*n^2 + (4/15)*n.

%F Conjectures from _Colin Barker_, Aug 21 2017: (Start)

%F G.f.: 2*x*(3 + 52*x + 156*x^2 + 124*x^3 + 25*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....4....3....2....0....4....1....4....0....5....4....4....2....3....1....3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 20 2014