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A220031 Number of n X 7 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 7 array.

%I A220031 #7 Jul 30 2018 06:14:21
%S A220031 7,18,55,137,302,613,1165,2094,3587,5893,9335,14323,21368,31097,44269,
%T A220031 61792,84741,114377,152167,199805,259234,332669,422621,531922,663751,
%U A220031 821661,1009607,1231975,1493612,1799857,2156573,2570180,3047689,3596737
%N A220031 Number of n X 7 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 7 array.
%C A220031 Column 7 of A220032.
%H A220031 R. H. Hardin, <a href="/A220031/b220031.txt">Table of n, a(n) for n = 1..68</a>
%F A220031 Empirical: a(n) = (1/720)*n^6 + (7/240)*n^5 + (11/144)*n^4 + (25/48)*n^3 + (263/90)*n^2 + (29/20)*n - 4 for n>2.
%F A220031 Conjectures from _Colin Barker_, Jul 30 2018: (Start)
%F A220031 G.f.: x*(7 - 31*x + 76*x^2 - 115*x^3 + 113*x^4 - 66*x^5 + 17*x^6 + x^7 - x^8) / (1 - x)^7.
%F A220031 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.
%F A220031 (End)
%e A220031 Some solutions for n=3:
%e A220031 ..1..1..0..0..0..0..0....1..1..1..0..0..0..0....1..0..0..0..0..0..0
%e A220031 ..1..1..0..0..0..0..0....1..1..1..1..1..0..0....1..1..1..0..0..0..0
%e A220031 ..1..1..0..0..0..0..0....1..1..1..1..1..0..0....1..1..1..1..0..0..0
%Y A220031 Cf. A220032.
%K A220031 nonn
%O A220031 1,1
%A A220031 _R. H. Hardin_, Dec 03 2012