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A241620 Number of length 5+2 0..n arrays with no consecutive three elements summing to more than n. 1

%I

%S 19,147,711,2567,7586,19374,44274,92697,180829,332761,583089,980031,

%T 1589108,2497436,3818676,5698689,8321943,11918719,16773163,23232231,

%U 31715574,42726410,56863430,74833785,97467201,125731269,160747957

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

%H R. H. Hardin, <a href="/A241620/b241620.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Conjectures from _Colin Barker_, Oct 30 2018: (Start)

%F 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 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 ..3....3....1....0....2....2....2....3....0....0....0....2....1....5....0....0

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

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

%e ..0....0....1....0....1....1....2....1....1....0....0....1....0....0....1....2

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

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

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

%Y Row 5 of A241619.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 26 2014

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Last modified March 29 05:31 EDT 2020. Contains 333105 sequences. (Running on oeis4.)