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%I #11 May 25 2021 05:09:59
%S 89,193,340,537,792,1114,1513,2000,2587,3287,4114,5083,6210,7512,9007,
%T 10714,12653,14845,17312,20077,23164,26598,30405,34612,39247,44339,
%U 49918,56015,62662,69892,77739,86238,95425,105337,116012,127489,139808,153010
%N Number of (n+2) X 4 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
%C Column 2 of A184548.
%H R. H. Hardin, <a href="/A184541/b184541.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (1/24)*n^4 + (3/4)*n^3 + (383/24)*n^2 + (201/4)*n + 22.
%F Conjectures from _Colin Barker_, Apr 12 2018: (Start)
%F G.f.: x*(89 - 252*x + 265*x^2 - 123*x^3 + 22*x^4) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for 6 X 4:
%e ..0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..1....0..0..0..1
%e ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..1
%e ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..1..1..1
%e ..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..1....0..1..1..1
%e ..0..0..1..0....0..0..1..0....0..1..0..0....0..0..0..1....1..1..1..1
%e ..0..1..1..0....0..0..1..1....1..1..0..0....0..0..0..1....1..1..1..1
%Y Cf. A184548.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 16 2011
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