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A266472 Number of 5 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.

%I A266472 #8 Jan 10 2019 08:08:32
%S A266472 6,19,67,232,735,2090,5371,12645,27639,56726,110334,204903,365538,
%T A266472 629531,1050952,1706538,2703140,4187021,6355333,9470138,13875377,
%U A266472 20017232,28468369,39956595,55398509,75938776,102995704,138313857,184024492
%N A266472 Number of 5 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
%H A266472 R. H. Hardin, <a href="/A266472/b266472.txt">Table of n, a(n) for n = 1..210</a>
%F A266472 Empirical: a(n) = (1/181440)*n^9 + (1/8064)*n^8 + (29/15120)*n^7 + (13/960)*n^6 + (301/8640)*n^5 + (101/384)*n^4 - (34619/90720)*n^3 + (37531/10080)*n^2 - (4171/2520)*n + 4.
%F A266472 Conjectures from _Colin Barker_, Jan 10 2019: (Start)
%F A266472 G.f.: x*(6 - 41*x + 147*x^2 - 303*x^3 + 410*x^4 - 382*x^5 + 248*x^6 - 109*x^7 + 30*x^8 - 4*x^9) / (1 - x)^10.
%F A266472 a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
%F A266472 (End)
%e A266472 Some solutions for n=4:
%e A266472 ..0..0..1..1....0..1..1..1....0..0..0..1....0..0..0..1....0..1..1..1
%e A266472 ..0..1..0..0....1..0..0..0....0..1..1..1....0..1..1..0....1..0..0..1
%e A266472 ..1..0..0..0....1..0..0..1....1..0..1..0....0..1..1..0....1..0..1..0
%e A266472 ..1..0..0..0....1..0..1..0....1..1..0..0....1..0..0..0....1..1..0..0
%e A266472 ..1..0..0..0....1..1..0..0....1..1..1..0....1..0..0..1....1..1..1..1
%Y A266472 Row 5 of A266470.
%K A266472 nonn
%O A266472 1,1
%A A266472 _R. H. Hardin_, Dec 29 2015