A250017 - OEIS

%I #8 Nov 10 2018 12:44:08

%S 20,912,13512,106352,558588,2224848,7259024,20384352,50937444,

%T 115954256,244606296,484335696,909078092,1630002576,2809238304,

%U 4677097664,7553346228,11873110032,18218051048,27353482032,40272132252,58245315920

%N Number of length 3+5 0..n arrays with no six consecutive terms having the maximum of any three terms equal to the minimum of the remaining three terms.

%H R. H. Hardin, <a href="/A250017/b250017.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^8 + (41/35)*n^7 + (56/15)*n^6 + (22/5)*n^5 + (19/3)*n^4 + (17/5)*n^3 - (16/15)*n^2 + (36/35)*n.

%F Conjectures from _Colin Barker_, Nov 10 2018: (Start)

%F G.f.: 4*x*(5 + 183*x + 1506*x^2 + 3974*x^3 + 3441*x^4 + 903*x^5 + 68*x^6) / (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>8.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%e ..1....4....1....0....0....0....0....0....0....0....3....4....0....1....0....4

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

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

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

%Y Row 3 of A250014.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 10 2014