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%I #8 Sep 07 2018 03:04:37
%S 7,29,99,302,842,2177,5281,12128,26548,55684,112389,219051,413531,
%T 758154,1353017,2355283,4006629,6671623,10890535,17450956,27483624,
%U 42589055,65002969,97810106,145217866,212903302,308449369,441889009,626378657
%N Number of n X 3 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 4 binary array with rows and columns of the latter in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A227086/b227086.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/39916800)*n^11 + (1/3628800)*n^10 + (1/120960)*n^9 + (1/8640)*n^8 + (1481/1209600)*n^7 + (1153/172800)*n^6 + (14807/181440)*n^5 + (92843/362880)*n^4 + (10901/16800)*n^3 + (19709/7200)*n^2 + (20959/9240)*n + 1.
%F Conjectures from _Colin Barker_, Sep 07 2018: (Start)
%F G.f.: x*(7 - 55*x + 213*x^2 - 512*x^3 + 837*x^4 - 964*x^5 + 794*x^6 - 468*x^7 + 197*x^8 - 58*x^9 + 11*x^10 - x^11) / (1 - x)^12.
%F a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12.
%F (End)
%e Some solutions for n=4:
%e ..1..0..0....1..1..0....0..1..0....0..0..0....0..0..0....0..1..0....0..0..1
%e ..0..0..0....1..0..0....1..1..0....0..0..0....0..1..0....1..1..0....0..1..1
%e ..0..0..0....0..0..1....1..0..1....0..0..0....0..1..0....1..0..0....0..0..0
%e ..0..0..0....0..0..1....0..1..1....0..0..0....0..0..0....0..0..1....1..1..0
%Y Column 3 of A227089.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 30 2013
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