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A201372 Number of n X 5 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.

%I A201372 #12 May 22 2018 20:37:20
%S A201372 2,6,22,80,268,786,2016,4608,9582,18446,33330,57136,93704,147994,
%T A201372 226284,336384,487866,692310,963566,1318032,1774948,2356706,3089176,
%U A201372 4002048,5129190,6509022,8184906,10205552,12625440,15505258,18912356,22921216
%N A201372 Number of n X 5 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.
%C A201372 Column 5 of A201375.
%H A201372 R. H. Hardin, <a href="/A201372/b201372.txt">Table of n, a(n) for n = 1..210</a>
%F A201372 Empirical: a(n) = (1/45)*n^6 - (1/60)*n^5 - (4/9)*n^4 + (11/4)*n^3 - (206/45)*n^2 + (64/15)*n.
%F A201372 Conjectures from _Colin Barker_, May 22 2018: (Start)
%F A201372 G.f.: 2*x*(1 - 4*x + 11*x^2 - 9*x^3 + 15*x^4 - 6*x^5) / (1 - x)^7.
%F A201372 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>7.
%F A201372 (End)
%e A201372 Some solutions for n=6:
%e A201372 ..0..1..1..1..1....0..0..0..1..1....0..0..0..1..1....0..0..0..1..1
%e A201372 ..0..1..1..1..1....0..0..1..0..1....0..0..1..0..1....0..0..0..1..1
%e A201372 ..0..1..1..1..1....0..1..1..1..0....0..1..0..1..0....0..1..1..0..1
%e A201372 ..1..0..1..1..1....1..0..1..0..0....0..1..1..0..0....0..1..1..1..0
%e A201372 ..1..1..0..0..1....1..1..0..0..0....0..1..1..0..0....1..0..1..1..0
%e A201372 ..1..1..1..1..0....1..1..0..0..0....1..0..0..0..0....1..1..0..0..0
%Y A201372 Cf. A201375.
%K A201372 nonn
%O A201372 1,1
%A A201372 _R. H. Hardin_, Nov 30 2011