A249884 - OEIS

%I #8 Nov 10 2018 05:46:31

%S 35,805,7420,40740,161315,510965,1377040,3284400,7120155,14296205,

%T 26954620,48220900,82510155,135891245,216513920,335104000,505531635,

%U 745457685,1077063260,1527867460,2131638355,2929402245,3970556240

%N Number of length 1+6 0..n arrays with no seven consecutive terms having the maximum of any three terms equal to the minimum of the remaining four terms.

%H R. H. Hardin, <a href="/A249884/b249884.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^7 + (7/2)*n^6 + 7*n^5 + (35/4)*n^4 + (49/6)*n^3 + (21/4)*n^2 + (4/3)*n.

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

%F G.f.: 35*x*(1 + x)*(1 + 4*x + x^2)*(1 + 10*x + x^2) / (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 ..2....1....1....0....2....0....0....1....0....4....0....2....0....2....1....1

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

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

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

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

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

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

%Y Row 1 of A249883.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2014