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%I #8 Oct 31 2018 09:24:13
%S 43,509,3150,13339,44063,122162,297324,654345,1329163,2529175,4558346,
%T 7847619,12991135,20788772,32295512,48878145,72279819,104692945,
%U 148840966,208069499,286447359,388877974,521221700,690429545,904688811
%N Number of length 3+4 0..n arrays with no consecutive five elements summing to more than 2*n.
%H R. H. Hardin, <a href="/A241939/b241939.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (509/5040)*n^7 + 1*n^6 + (743/180)*n^5 + (223/24)*n^4 + (8993/720)*n^3 + (245/24)*n^2 + (502/105)*n + 1.
%F Conjectures from _Colin Barker_, Oct 30 2018: (Start)
%F G.f.: x*(43 + 165*x + 282*x^2 - 17*x^3 + 57*x^4 - 28*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 ..1....0....1....4....0....1....2....2....0....0....2....1....1....1....4....1
%e ..3....2....4....0....0....3....0....0....2....0....1....1....0....1....1....1
%e ..2....0....1....0....0....0....1....3....1....0....2....0....0....1....0....0
%e ..0....2....0....0....1....0....2....2....4....4....0....0....2....0....0....4
%e ..1....3....2....2....1....1....0....1....0....0....2....0....2....2....0....0
%e ..0....0....0....3....4....3....1....1....1....0....2....1....2....1....1....0
%e ..0....1....4....3....1....0....4....1....2....1....1....4....0....1....0....3
%Y Row 3 of A241936.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 02 2014
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