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A184545 Number of (n+2) X 8 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

%I A184545 #12 Apr 14 2018 02:37:12
%S A184545 415,1114,2413,4774,8989,16345,28844,49489,82648,134509,213640,331669,
%T A184545 504100,751282,1099549,1582550,2242789,3133396,4320151,5883784,
%U A184545 7922575,10555279,13924402,18199855,23583014,30311215,38662714,48962143,61586494
%N A184545 Number of (n+2) X 8 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
%C A184545 Column 6 of A184548.
%H A184545 R. H. Hardin, <a href="/A184545/b184545.txt">Table of n, a(n) for n = 1..200</a>
%F A184545 Empirical: a(n) = (1/40320)*n^8 + (13/10080)*n^7 + (83/2880)*n^6 + (13/36)*n^5 + (15967/5760)*n^4 + (19201/1440)*n^3 + (121183/1120)*n^2 + (12673/56)*n + 64.
%F A184545 Conjectures from _Colin Barker_, Apr 13 2018: (Start)
%F A184545 G.f.: x*(415 - 2621*x + 7327*x^2 - 11699*x^3 + 11605*x^4 - 7310*x^5 + 2861*x^6 - 641*x^7 + 64*x^8) / (1 - x)^9.
%F A184545 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F A184545 (End)
%e A184545 Some solutions for 4 X 8:
%e A184545   0 0 0 0 0 0 0 0     0 0 0 0 0 0 0 0     0 0 0 0 0 0 0 0
%e A184545   0 0 0 0 0 0 1 1     0 0 0 0 0 0 0 0     0 0 0 0 0 0 1 1
%e A184545   0 0 0 0 0 1 0 1     0 0 0 0 0 0 1 1     0 0 0 0 0 1 0 0
%e A184545   0 0 0 1 1 1 1 1     0 0 0 1 1 1 0 0     0 0 0 0 0 1 1 1
%Y A184545 Cf. A184548.
%K A184545 nonn
%O A184545 1,1
%A A184545 _R. H. Hardin_, Jan 16 2011