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%I #7 Sep 09 2018 17:17:32
%S 4,16,50,131,301,625,1198,2153,3670,5986,9406,14315,21191,30619,43306,
%T 60097,81992,110164,145978,191011,247073,316229,400822,503497,627226,
%U 775334,951526,1159915,1405051,1691951,2026130,2413633,2861068,3375640
%N Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having an odd sum, with rows and columns of the latter in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A227675/b227675.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (29/144)*n^4 + (5/16)*n^3 + (647/360)*n^2 + (2/3)*n + 1.
%F Conjectures from _Colin Barker_, Sep 09 2018: (Start)
%F G.f.: x*(4 - 12*x + 22*x^2 - 23*x^3 + 14*x^4 - 5*x^5 + x^6) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=4.
%e ..1..0....1..0....0..0....0..0....1..0....0..1....0..1....0..0....0..0....0..1
%e ..1..0....0..0....0..1....0..1....0..1....1..1....1..1....0..0....1..0....1..1
%e ..0..0....0..1....1..0....1..1....0..0....1..1....1..0....0..1....0..0....0..0
%e ..0..0....0..1....1..0....1..1....0..0....0..1....0..0....1..1....0..1....0..0
%Y Column 2 of A227679.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 19 2013
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