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%I #8 Sep 07 2018 03:04:26
%S 4,12,29,62,122,225,393,655,1048,1618,2421,3524,5006,6959,9489,12717,
%T 16780,21832,28045,35610,44738,55661,68633,83931,101856,122734,146917,
%U 174784,206742,243227,284705,331673,384660,444228,510973,585526,668554
%N Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically increasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A227085/b227085.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (5/24)*n^3 + (35/24)*n^2 + (77/60)*n + 1.
%F Conjectures from _Colin Barker_, Sep 07 2018: (Start)
%F G.f.: x*(2 - x)*(2 - 5*x + 6*x^2 - 3*x^3 + x^4) / (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>6.
%F (End)
%e Some solutions for n=4:
%e ..0..0....1..1....1..0....1..1....0..0....0..0....1..0....0..0....1..0....1..0
%e ..0..0....1..0....0..1....1..0....0..0....0..0....1..0....0..1....0..0....0..0
%e ..0..1....0..0....0..0....0..0....0..0....0..1....0..0....0..1....0..0....0..1
%e ..1..1....0..1....0..1....0..0....0..1....0..1....0..0....0..0....0..0....0..0
%Y Column 2 of A227089.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 30 2013
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