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%I #8 Apr 13 2018 08:45:54
%S 147,340,631,1048,1627,2413,3461,4837,6619,8898,11779,15382,19843,
%T 25315,31969,39995,49603,61024,74511,90340,108811,130249,155005,
%U 183457,216011,253102,295195,342786,396403,456607,523993,599191,682867,775724,878503
%N Number of (n+2) X 5 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
%C Column 3 of A184548.
%H R. H. Hardin, <a href="/A184542/b184542.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (1/120)*n^5 + (5/24)*n^4 + (49/24)*n^3 + (739/24)*n^2 + (1659/20)*n + 31.
%F Conjectures from _Colin Barker_, Apr 13 2018: (Start)
%F G.f.: x*(147 - 542*x + 796*x^2 - 578*x^3 + 209*x^4 - 31*x^5) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.
%F (End)
%e Some solutions for 4 X 5:
%e ..0..0..0..0..0....0..0..0..0..1....0..0..0..0..0....0..0..0..0..0
%e ..0..0..0..1..1....0..0..0..0..1....0..0..0..1..1....0..0..0..0..1
%e ..0..0..1..0..0....0..0..1..1..1....0..1..1..0..0....0..0..1..1..0
%e ..0..0..1..1..1....0..1..1..1..1....1..1..1..1..1....0..1..1..1..0
%Y Cf. A184548.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 16 2011
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