A254703 - OEIS

%I #8 Dec 18 2018 09:24:41

%S 136,2310,16276,72271,242076,670372,1618264,3520845,7060672,13259026,

%T 23586828,40097083,65580724,103747728,159435376,238845529,349812792,

%U 502105438,707760964,981458151,1340927500,1807401916,2406109512

%N Number of length 5+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="/A254703/b254703.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (13/35)*n^7 + (13/2)*n^6 + 26*n^5 + 41*n^4 + (327/10)*n^3 + (39/2)*n^2 + (125/14)*n + 1.

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

%F G.f.: x*(136 + 1222*x + 1604*x^2 - 873*x^3 - 204*x^4 - 20*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=4:

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

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

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

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

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

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

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

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

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

%Y Row 5 of A254698.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 05 2015