A254702 - OEIS

%I #7 Dec 17 2018 09:43:44

%S 86,1140,6808,26759,81390,208114,469376,962541,1831798,3282224,

%T 5596152,9151987,14445614,22114542,32964928,48001625,68461398,

%U 95849452,131979416,179016927,239526958,316525034,413532480,534635845,684550646,868689576

%N Number of length 4+4 0..n arrays with every five consecutive terms having the maximum of some two terms equal to the minimum of the remaining three terms.

%H R. H. Hardin, <a href="/A254702/b254702.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/35)*n^7 + (8/5)*n^6 + (56/5)*n^5 + 25*n^4 + (249/10)*n^3 + (77/5)*n^2 + (481/70)*n + 1.

%F Conjectures from _Colin Barker_, Dec 17 2018: (Start)

%F G.f.: x*(86 + 452*x + 96*x^2 - 601*x^3 + 122*x^4 - 18*x^5 + 8*x^6 - x^7) / (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 ..3....1....3....0....2....1....0....4....4....4....4....3....4....2....0....3

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

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

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

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

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

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

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

%Y Row 4 of A254698.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 05 2015