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A219498 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 4 array.

%I A219498 #8 Jul 26 2018 06:35:00
%S A219498 4,7,18,35,58,88,126,173,230,298,378,471,578,700,838,993,1166,1358,
%T A219498 1570,1803,2058,2336,2638,2965,3318,3698,4106,4543,5010,5508,6038,
%U A219498 6601,7198,7830,8498,9203,9946,10728,11550,12413,13318,14266,15258,16295,17378
%N A219498 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 4 array.
%C A219498 Column 4 of A219502.
%H A219498 R. H. Hardin, <a href="/A219498/b219498.txt">Table of n, a(n) for n = 1..210</a>
%F A219498 Empirical: a(n) = (1/6)*n^3 + 1*n^2 + (23/6)*n - 7 for n>2.
%F A219498 Conjectures from _Colin Barker_, Jul 26 2018: (Start)
%F A219498 G.f.: x*(4 - 9*x + 14*x^2 - 11*x^3 + 2*x^4 + x^5) / (1 - x)^4.
%F A219498 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
%F A219498 (End)
%e A219498 Some solutions for n=3:
%e A219498 ..0..0..0..0....1..1..0..0....0..0..0..0....1..0..0..0....1..1..0..0
%e A219498 ..1..0..0..0....1..1..1..0....1..0..0..0....1..0..0..0....1..1..0..0
%e A219498 ..1..0..0..0....1..1..1..1....1..1..1..0....1..0..0..0....1..1..1..0
%Y A219498 Cf. A219502.
%K A219498 nonn
%O A219498 1,1
%A A219498 _R. H. Hardin_, Nov 20 2012