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A241620 Number of length 5+2 0..n arrays with no consecutive three elements summing to more than n.

%I A241620 #8 Oct 30 2018 10:34:37
%S A241620 19,147,711,2567,7586,19374,44274,92697,180829,332761,583089,980031,
%T A241620 1589108,2497436,3818676,5698689,8321943,11918719,16773163,23232231,
%U A241620 31715574,42726410,56863430,74833785,97467201,125731269,160747957
%N A241620 Number of length 5+2 0..n arrays with no consecutive three elements summing to more than n.
%H A241620 R. H. Hardin, <a href="/A241620/b241620.txt">Table of n, a(n) for n = 1..210</a>
%F A241620 Empirical: a(n) = (47/5040)*n^7 + (47/360)*n^6 + (7/9)*n^5 + (23/9)*n^4 + (3599/720)*n^3 + (2093/360)*n^2 + (26/7)*n + 1.
%F A241620 Conjectures from _Colin Barker_, Oct 30 2018: (Start)
%F A241620 G.f.: x*(19 - 5*x + 67*x^2 - 69*x^3 + 56*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F A241620 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 A241620 (End)
%e A241620 Some solutions for n=5:
%e A241620 ..3....3....1....0....2....2....2....3....0....0....0....2....1....5....0....0
%e A241620 ..2....2....3....3....2....0....1....2....3....3....5....0....1....0....1....0
%e A241620 ..0....0....1....0....1....3....0....0....1....0....0....2....3....0....1....2
%e A241620 ..0....0....1....0....1....1....2....1....1....0....0....1....0....0....1....2
%e A241620 ..2....1....0....3....0....1....1....3....1....0....4....0....1....0....1....1
%e A241620 ..0....3....0....0....0....1....0....0....2....2....1....2....1....2....1....0
%e A241620 ..3....0....3....1....1....0....2....2....2....1....0....3....0....2....3....3
%Y A241620 Row 5 of A241619.
%K A241620 nonn
%O A241620 1,1
%A A241620 _R. H. Hardin_, Apr 26 2014