A250060 - OEIS

%I #8 Aug 22 2017 06:36:19

%S 21,735,7224,40320,160545,509691,1375080,3281544,7116165,14290815,

%T 26947536,48211800,82498689,135877035,216496560,335083056,505506645,

%U 745428159,1077028680,1527827280,2131592001,2929349115,3970495704

%N Number of length 1+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 1 of A250059.

%H R. H. Hardin, <a href="/A250060/b250060.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^7 + (7/2)*n^6 + 7*n^5 + (35/4)*n^4 + (7/2)*n^3 - (7/4)*n^2 - n.

%F Conjectures from _Colin Barker_, Aug 22 2017: (Start)

%F G.f.: 21*x*(1 + x)*(1 + 26*x + 66*x^2 + 26*x^3 + x^4) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=5:

%e ..4....2....1....2....0....2....4....2....1....2....1....1....2....2....1....1

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 11 2014