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A220029 Number of n X 5 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 n X 5 array.

%I A220029 #7 Jul 30 2018 05:51:38
%S A220029 5,12,30,61,111,187,297,450,656,926,1272,1707,2245,2901,3691,4632,
%T A220029 5742,7040,8546,10281,12267,14527,17085,19966,23196,26802,30812,35255,
%U A220029 40161,45561,51487,57972,65050,72756,81126,90197,100007,110595,122001,134266
%N A220029 Number of n X 5 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 n X 5 array.
%C A220029 Column 5 of A220032.
%H A220029 R. H. Hardin, <a href="/A220029/b220029.txt">Table of n, a(n) for n = 1..210</a>
%F A220029 Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (61/12)*n - 4 for n>1.
%F A220029 Conjectures from _Colin Barker_, Jul 30 2018: (Start)
%F A220029 G.f.: x*(5 - 13*x + 20*x^2 - 19*x^3 + 11*x^4 - 3*x^5) / (1 - x)^5.
%F A220029 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
%F A220029 (End)
%e A220029 Some solutions for n=3:
%e A220029 ..0..0..0..0..0....0..0..0..0..0....1..0..0..0..0....1..0..0..0..0
%e A220029 ..1..0..0..0..0....1..1..0..0..0....1..0..0..0..0....1..1..0..0..0
%e A220029 ..1..1..1..0..0....1..1..1..0..0....1..1..1..0..0....1..1..0..0..0
%Y A220029 Cf. A220032.
%K A220029 nonn
%O A220029 1,1
%A A220029 _R. H. Hardin_, Dec 03 2012