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%I #8 Oct 30 2018 12:52:33
%S 28,287,1730,7483,25774,75180,193194,449295,963886,1934647,3672032,
%T 6645821,11544820,19351984,31437420,49671909,76563768,115422055,
%U 170549302,247467143,353178386,496469260,688255750,941978115,1274047866
%N Number of length 6+2 0..n arrays with no consecutive three elements summing to more than n.
%H R. H. Hardin, <a href="/A241621/b241621.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (13/2880)*n^8 + (13/180)*n^7 + (145/288)*n^6 + (719/360)*n^5 + (14197/2880)*n^4 + (2789/360)*n^3 + (121/16)*n^2 + (251/60)*n + 1.
%F Conjectures from _Colin Barker_, Oct 30 2018: (Start)
%F G.f.: x*(28 + 35*x + 155*x^2 - 107*x^3 + 127*x^4 - 84*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F (End)
%e Some solutions for n=5:
%e ..2....4....0....0....2....1....1....0....0....0....1....1....1....2....0....0
%e ..1....0....3....3....2....3....1....3....3....2....3....2....3....0....0....2
%e ..0....0....1....1....1....0....0....1....1....0....0....1....0....2....4....0
%e ..3....5....1....0....0....0....2....0....1....0....2....2....2....1....0....0
%e ..0....0....3....2....0....1....0....0....2....2....0....0....0....1....1....2
%e ..1....0....0....0....1....1....0....0....0....3....0....0....1....0....0....1
%e ..3....2....1....1....0....1....5....3....2....0....3....2....0....1....0....2
%e ..1....2....2....0....1....1....0....2....1....2....1....0....1....0....4....0
%Y Row 6 of A241619.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 26 2014
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