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A249963 Number of length 3+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. 1

%I

%S 15,897,14094,111746,585069,2319123,7532380,21069828,52478667,

%T 119135973,250738026,495501318,928465577,1662329463,2861289912,

%U 4758396424,7676971911,12056692041,18484955334,27734216586,40805996517,58982320859

%N Number of length 3+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 3 of A249960.

%H R. H. Hardin, <a href="/A249963/b249963.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^8 + (152/105)*n^7 + (62/15)*n^6 + (26/5)*n^5 + (1/2)*n^4 + (19/15)*n^3 + (28/15)*n^2 - (29/70)*n.

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

%F G.f.: x*(15 + 762*x + 6561*x^2 + 15932*x^3 + 13281*x^4 + 3594*x^5 + 175*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>9.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 09 2014

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Last modified March 4 03:53 EST 2021. Contains 341779 sequences. (Running on oeis4.)