%I #7 Sep 06 2018 10:56:54
%S 10,42,120,313,729,1556,3099,5818,10384,17744,29198,46489,71907,
%T 108408,159749,230640,326914,455716,625712,847319,1132957,1497324,
%U 1957695,2534246,3250404,4133224,5213794,6527669,8115335,10022704,12301641
%N Number of n X 2 0..4 arrays of sums of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A226988/b226988.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/5040)*n^7 + (1/180)*n^6 + (1/18)*n^5 + (11/36)*n^4 + (877/720)*n^3 + (287/90)*n^2 + (439/84)*n + 4 for n>4.
%F Conjectures from _Colin Barker_, Sep 06 2018: (Start)
%F G.f.: x*(10 - 38*x + 64*x^2 - 31*x^3 - 67*x^4 + 148*x^5 - 137*x^6 + 56*x^7 + 12*x^8 - 26*x^9 + 12*x^10 - 2*x^11) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>12.
%F (End)
%e Some solutions for n=4:
%e ..1..3....0..2....0..2....2..4....1..2....1..2....0..0....0..2....0..0....1..2
%e ..2..3....2..2....1..2....2..2....3..4....2..2....1..2....1..2....1..2....2..2
%e ..2..2....4..2....2..3....3..2....4..4....2..0....2..3....2..3....2..2....2..1
%e ..2..2....4..2....2..4....4..4....4..4....3..2....2..2....2..2....3..2....2..0
%Y Column 2 of A226992.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 25 2013