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A241620
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Number of length 5+2 0..n arrays with no consecutive three elements summing to more than n.
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1
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19, 147, 711, 2567, 7586, 19374, 44274, 92697, 180829, 332761, 583089, 980031, 1589108, 2497436, 3818676, 5698689, 8321943, 11918719, 16773163, 23232231, 31715574, 42726410, 56863430, 74833785, 97467201, 125731269, 160747957
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OFFSET
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1,1
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LINKS
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FORMULA
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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.
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.
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.
(End)
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EXAMPLE
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Some solutions for n=5:
..3....3....1....0....2....2....2....3....0....0....0....2....1....5....0....0
..2....2....3....3....2....0....1....2....3....3....5....0....1....0....1....0
..0....0....1....0....1....3....0....0....1....0....0....2....3....0....1....2
..0....0....1....0....1....1....2....1....1....0....0....1....0....0....1....2
..2....1....0....3....0....1....1....3....1....0....4....0....1....0....1....1
..0....3....0....0....0....1....0....0....2....2....1....2....1....2....1....0
..3....0....3....1....1....0....2....2....2....1....0....3....0....2....3....3
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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