A250374 - OEIS

%I #7 Nov 13 2018 12:48:36

%S 93,1382,8964,37385,118621,312578,720112,1498569,2879845,5190966,

%T 8877188,14527617,22903349,34968130,51921536,75234673,106688397,

%U 148414054,202936740,273221081,362719533,475423202,615915184,789426425,1001894101

%N Number of length 1+6 0..n arrays with every seven consecutive terms having the maximum of some three terms equal to the minimum of the remaining four terms.

%H R. H. Hardin, <a href="/A250374/b250374.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (7/2)*n^6 + 14*n^5 + (105/4)*n^4 + (161/6)*n^3 + (63/4)*n^2 + (17/3)*n + 1.

%F Conjectures from _Colin Barker_, Nov 13 2018: (Start)

%F G.f.: x*(93 + 731*x + 1243*x^2 + 404*x^3 + 55*x^4 - 7*x^5 + x^6) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=5:

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

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

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

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

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

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

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

%Y Row 1 of A250373.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 19 2014