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Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.

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`%I #8 Jul 28 2018 10:43:27
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`%S 3,6,16,33,61,106,176,281,433,646,936,1321,1821,2458,3256,4241,5441,
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`%T 6886,8608,10641,13021,15786,18976,22633,26801,31526,36856,42841,
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`%U 49533,56986,65256,74401,84481,95558,107696,120961,135421,151146,168208,186681
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`%N Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
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`%C Column 2 of A219816.
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`%H R. H. Hardin, <a href="/A219810/b219810.txt">Table of n, a(n) for n = 1..210</a>
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`%F Empirical: a(n) = (1/12)*n^4 - (1/2)*n^3 + (41/12)*n^2 - 3*n + 1 for n>1.
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`%F Conjectures from _Colin Barker_, Jul 28 2018: (Start)
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`%F G.f.: x*(3 - 9*x + 16*x^2 - 17*x^3 + 11*x^4 - 2*x^5) / (1 - x)^5.
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`%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
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`%F (End)
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`%e Some solutions for n=3:
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`%e ..1..1....0..0....0..0....0..0....0..0....1..1....2..2....0..0....1..1....0..0
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`%e ..2..1....0..0....0..0....0..0....0..0....1..1....2..2....0..0....1..1....1..0
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`%e ..2..2....2..0....1..0....0..0....1..1....2..1....2..2....2..1....2..2....2..2
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`%Y Cf. A219816.
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`%K nonn
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`%O 1,1
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`%A _R. H. Hardin_, Nov 28 2012
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