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A220034 Number of 4 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 4 X n array.

%I A220034 #7 Jul 30 2018 07:39:59
%S A220034 5,8,15,34,61,95,137,187,246,315,395,487,592,711,845,995,1162,1347,
%T A220034 1551,1775,2020,2287,2577,2891,3230,3595,3987,4407,4856,5335,5845,
%U A220034 6387,6962,7571,8215,8895,9612,10367,11161,11995,12870,13787,14747,15751,16800
%N A220034 Number of 4 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 4 X n array.
%C A220034 Row 4 of A220032.
%H A220034 R. H. Hardin, <a href="/A220034/b220034.txt">Table of n, a(n) for n = 1..210</a>
%F A220034 Empirical: a(n) = (1/6)*n^3 + (1/2)*n^2 + (43/3)*n - 45 for n>5.
%F A220034 Conjectures from _Colin Barker_, Jul 30 2018: (Start)
%F A220034 G.f.: x*(5 - 12*x + 13*x^2 + 2*x^3 - 12*x^4 + 3*x^5 + 2*x^6 - x^7 + x^8) / (1 - x)^4.
%F A220034 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>9.
%F A220034 (End)
%e A220034 Some solutions for n=3:
%e A220034 ..0..0..0....0..0..0....1..0..0....0..0..0....0..0..0....1..1..1....0..0..0
%e A220034 ..1..1..0....1..0..0....1..0..0....0..0..0....0..0..0....1..1..1....1..0..0
%e A220034 ..1..1..1....1..1..1....1..1..1....0..0..0....0..0..0....1..1..1....1..0..0
%e A220034 ..1..1..1....1..1..1....1..1..1....1..1..0....0..0..0....1..1..1....1..0..0
%Y A220034 Cf. A220032.
%K A220034 nonn
%O A220034 1,1
%A A220034 _R. H. Hardin_, Dec 03 2012