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A184540 Number of (n+2) X 3 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

%I A184540 #9 Apr 12 2018 22:24:34
%S A184540 45,89,147,220,309,415,539,682,845,1029,1235,1464,1717,1995,2299,2630,
%T A184540 2989,3377,3795,4244,4725,5239,5787,6370,6989,7645,8339,9072,9845,
%U A184540 10659,11515,12414,13357,14345,15379,16460,17589,18767,19995,21274,22605,23989
%N A184540 Number of (n+2) X 3 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
%C A184540 Column 1 of A184548.
%H A184540 R. H. Hardin, <a href="/A184540/b184540.txt">Table of n, a(n) for n = 1..200</a>
%F A184540 Empirical: a(n) = (84 + 149*n + 36*n^2 + n^3) / 6. Corrected by _Colin Barker_, Apr 12 2018~
%F A184540 Conjectures from _Colin Barker_, Apr 12 2018: (Start)
%F A184540 G.f.: x*(45 - 91*x + 61*x^2 - 14*x^3) / (1 - x)^4.
%F A184540 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A184540 (End)
%e A184540 Some solutions for 4 X 3:
%e A184540 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A184540 ..0..0..1....0..1..1....0..0..0....0..0..1....0..0..1....0..1..1....0..0..1
%e A184540 ..0..1..1....0..1..1....0..0..1....1..1..1....0..1..1....0..1..1....1..1..0
%e A184540 ..1..0..1....1..0..0....0..1..0....1..1..1....1..1..0....0..1..1....1..1..1
%Y A184540 Cf. A184548.
%K A184540 nonn
%O A184540 1,1
%A A184540 _R. H. Hardin_, Jan 16 2011