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%I A219853 #7 Jul 28 2018 12:16:04
%S A219853 6,7,17,33,56,86,125,173,230,296,371,455,548,650,761,881,1010,1148,
%T A219853 1295,1451,1616,1790,1973,2165,2366,2576,2795,3023,3260,3506,3761,
%U A219853 4025,4298,4580,4871,5171,5480,5798,6125,6461,6806,7160,7523,7895,8276,8666,9065
%N A219853 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 2 X n array.
%C A219853 Row 2 of A219852.
%H A219853 R. H. Hardin, <a href="/A219853/b219853.txt">Table of n, a(n) for n = 1..210</a>
%F A219853 Empirical: a(n) = (9/2)*n^2 - (39/2)*n + 41 for n>4.
%F A219853 Conjectures from _Colin Barker_, Jul 28 2018: (Start)
%F A219853 G.f.: x*(6 - 11*x + 14*x^2 - 3*x^3 + x^4 + 2*x^6) / (1 - x)^3.
%F A219853 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
%F A219853 (End)
%e A219853 Some solutions for n=3:
%e A219853 ..0..0..0....1..0..0....2..1..1....1..1..1....1..1..1....2..0..0....0..0..0
%e A219853 ..0..0..1....1..0..2....2..1..2....1..1..1....1..0..0....2..0..2....0..0..0
%Y A219853 Cf. A219852.
%K A219853 nonn
%O A219853 1,1
%A A219853 _R. H. Hardin_, Nov 29 2012

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