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A219499 Number of n X 5 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 5 array.

%I A219499 #8 Jul 26 2018 06:35:05
%S A219499 5,9,26,58,107,179,281,421,608,852,1164,1556,2041,2633,3347,4199,5206,
%T A219499 6386,7758,9342,11159,13231,15581,18233,21212,24544,28256,32376,36933,
%U A219499 41957,47479,53531,60146,67358,75202,83714,92931,102891,113633,125197
%N A219499 Number of n X 5 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 5 array.
%C A219499 Column 5 of A219502.
%H A219499 R. H. Hardin, <a href="/A219499/b219499.txt">Table of n, a(n) for n = 1..210</a>
%F A219499 Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (35/24)*n^2 + (21/4)*n - 13 for n>2.
%F A219499 Conjectures from _Colin Barker_, Jul 26 2018: (Start)
%F A219499 G.f.: x*(5 - 16*x + 31*x^2 - 32*x^3 + 12*x^4 + 4*x^5 - 3*x^6) / (1 - x)^5.
%F A219499 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 A219499 (End)
%e A219499 Some solutions for n=3:
%e A219499 ..1..0..0..0..0....0..0..0..0..0....1..1..1..0..0....0..0..0..0..0
%e A219499 ..1..0..0..0..0....1..0..0..0..0....1..1..1..1..0....1..0..0..0..0
%e A219499 ..1..1..0..0..0....1..1..1..1..1....1..1..1..1..1....1..1..1..0..0
%Y A219499 Cf. A219502.
%K A219499 nonn
%O A219499 1,1
%A A219499 _R. H. Hardin_, Nov 20 2012