A249967 - OEIS

%I #8 Aug 21 2017 22:53:23

%S 15,8823,709814,18707320,251002319,2149795141,13385651492,65717571120,

%T 268511791119,948021599547,2972106528666,8443442678840,22076610372895,

%U 53774915777897,123215084622184,267660712891040,554792683762767

%N Number of length 7+5 0..n arrays with no six consecutive terms having the maximum of any two terms equal to the minimum of the remaining four terms.

%C Row 7 of A249960.

%H R. H. Hardin, <a href="/A249967/b249967.txt">Table of n, a(n) for n = 1..42</a>

%F Empirical: a(n) = n^12 - (53/42)*n^11 + (1404/175)*n^10 - (8593/1260)*n^9 + (8647/1260)*n^8 + (3511/252)*n^7 - (43133/1800)*n^6 + (41323/2520)*n^5 + (21641/2520)*n^4 - (2225/168)*n^3 + (7339/1050)*n^2 - (158/105)*n.

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

%F G.f.: x*(15 + 8628*x + 596285*x^2 + 10163642*x^3 + 60659998*x^4 + 149218290*x^5 + 162389570*x^6 + 78777198*x^7 + 16029715*x^8 + 1141682*x^9 + 16577*x^10) / (1 - x)^13.

%F a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.

%F (End)

%e Some solutions for n=2:

%e ..0....1....2....2....0....1....2....0....0....0....1....0....1....0....0....2

%e ..2....1....2....0....2....2....0....2....2....2....0....2....0....0....2....2

%e ..0....2....0....2....2....0....2....1....0....1....0....2....1....1....2....2

%e ..2....2....0....2....1....0....2....2....2....2....1....2....2....1....0....1

%e ..1....2....1....1....2....1....2....1....2....2....1....1....0....2....2....0

%e ..2....2....1....2....2....1....0....0....2....2....1....0....2....2....1....0

%e ..2....0....1....0....1....2....1....0....0....0....1....2....2....0....0....1

%e ..2....1....1....2....2....2....2....2....1....0....0....2....2....0....2....2

%e ..0....0....0....2....2....0....0....2....0....1....0....0....1....2....1....2

%e ..0....1....0....0....0....0....1....2....1....1....2....1....2....1....0....2

%e ..1....2....1....1....2....2....2....1....2....1....1....1....1....1....2....2

%e ..1....2....1....2....2....1....0....2....2....1....1....0....2....1....2....1

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 09 2014