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A249712 Number of length 6+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

%I A249712 #8 Nov 10 2018 05:46:45
%S A249712 52,659,3440,11925,32500,75495,156416,297321,528340,889339,1431728,
%T A249712 2220413,3335892,4876495,6960768,9730001,13350900,18018403,23958640,
%U A249712 31432037,40736564,52211127,66239104,83252025,103733396,128222667
%N A249712 Number of length 6+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.
%H A249712 R. H. Hardin, <a href="/A249712/b249712.txt">Table of n, a(n) for n = 1..210</a>
%F A249712 Empirical: a(n) = (1/5)*n^6 + (73/15)*n^5 + 18*n^4 + 22*n^3 + (34/5)*n^2 - (13/15)*n + 1.
%F A249712 Conjectures from _Colin Barker_, Nov 10 2018: (Start)
%F A249712 G.f.: x*(52 + 295*x - 81*x^2 - 136*x^3 + 20*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A249712 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 A249712 (End)
%e A249712 Some solutions for n=6:
%e A249712 ..4....2....3....2....4....2....4....5....3....0....5....0....3....5....6....6
%e A249712 ..3....6....3....0....5....5....2....4....0....3....6....5....3....4....2....5
%e A249712 ..6....4....1....2....3....2....2....4....2....3....5....5....3....6....3....2
%e A249712 ..4....4....5....6....4....1....0....1....2....6....5....5....3....5....3....5
%e A249712 ..4....0....3....2....4....2....2....4....2....3....4....5....2....5....3....5
%e A249712 ..1....4....3....2....4....6....2....4....5....3....5....5....3....5....3....5
%e A249712 ..4....4....3....0....5....2....2....4....1....2....5....5....3....5....5....6
%e A249712 ..4....4....1....5....4....1....2....5....2....4....6....6....4....2....3....5
%e A249712 ..6....4....5....2....2....2....2....3....2....3....2....5....3....5....3....1
%Y A249712 Row 6 of A249707.
%K A249712 nonn
%O A249712 1,1
%A A249712 _R. H. Hardin_, Nov 04 2014