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A219680 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.

%I A219680 #7 Jul 26 2018 13:47:29
%S A219680 3,4,9,19,35,60,98,154,234,345,495,693,949,1274,1680,2180,2788,3519,
%T A219680 4389,5415,6615,8008,9614,11454,13550,15925,18603,21609,24969,28710,
%U A219680 32860,37448,42504,48059,54145,60795,68043,75924,84474,93730,103730,114513
%N A219680 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
%C A219680 Column 2 of A219686.
%H A219680 R. H. Hardin, <a href="/A219680/b219680.txt">Table of n, a(n) for n = 1..210</a>
%F A219680 Empirical: a(n) = (1/24)*n^4 - (1/4)*n^3 + (47/24)*n^2 - (7/4)*n for n>2.
%F A219680 Conjectures from _Colin Barker_, Jul 26 2018: (Start)
%F A219680 G.f.: x*(3 - 11*x + 19*x^2 - 16*x^3 + 5*x^4 + 2*x^5 - x^6) / (1 - x)^5.
%F A219680 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.
%F A219680 (End)
%e A219680 All solutions for n=3:
%e A219680 ..1..1....1..1....0..0....0..0....1..0....1..1....2..2....0..0....0..0
%e A219680 ..1..1....1..0....0..0....0..0....0..0....1..1....2..2....0..0....0..0
%e A219680 ..2..2....0..0....1..1....1..2....0..0....1..1....2..2....2..2....0..0
%Y A219680 Cf. A219686.
%K A219680 nonn
%O A219680 1,1
%A A219680 _R. H. Hardin_, Nov 25 2012