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A250145
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Number of length 6+2 0..n arrays with the medians of every three consecutive terms nondecreasing.
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1
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111, 2026, 16104, 81664, 311498, 974944, 2637228, 6376143, 14100493, 28998090, 56144452, 103306710, 181980592, 308701712, 506675752, 807775485, 1254955947, 1905142426, 2832649296, 4133191084, 5928550518, 8371971664, 11654349620
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..162
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FORMULA
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Empirical: a(n) = (1/12)*n^8 + (1487/1260)*n^7 + (4757/720)*n^6 + (13757/720)*n^5 + (4519/144)*n^4 + (21611/720)*n^3 + (2957/180)*n^2 + (2183/420)*n + 1.
Conjectures from Colin Barker, Nov 11 2018: (Start)
G.f.: x*(111 + 1027*x + 1866*x^2 + 340*x^3 + 68*x^4 - 80*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.
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>10.
(End)
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EXAMPLE
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Some solutions for n=4:
2 1 2 1 0 4 2 2 0 1 3 1 2 0 2 3
2 4 4 0 0 0 0 0 4 1 1 0 1 0 4 3
2 2 0 2 3 0 0 0 1 3 1 1 2 0 2 4
2 0 2 2 4 4 0 2 0 3 0 3 2 0 0 2
2 2 2 3 3 2 1 3 2 1 1 2 2 2 3 3
2 3 2 1 3 1 3 4 4 3 4 4 3 1 3 4
3 4 2 2 3 4 2 4 2 4 1 4 2 0 4 0
1 3 0 4 3 4 0 3 3 1 3 1 1 4 1 3
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CROSSREFS
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Row 6 of A250140.
Sequence in context: A303256 A137465 A101152 * A075859 A264466 A302384
Adjacent sequences: A250142 A250143 A250144 * A250146 A250147 A250148
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Nov 13 2014
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STATUS
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approved
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