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A184546 Number of (n+2) X 9 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

%I A184546 #9 Apr 14 2018 13:11:12
%S A184546 539,1513,3461,7307,14767,28844,54543,99872,177207,305112,510719,
%T A184546 832788,1325583,2063717,3148137,4713439,6936723,10048219,14343937,
%U A184546 20200617,28093279,38615698,52504155,70664842,94205327,124470514,163083563
%N A184546 Number of (n+2) X 9 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
%C A184546 Column 7 of A184548.
%H A184546 R. H. Hardin, <a href="/A184546/b184546.txt">Table of n, a(n) for n = 1..200</a>
%F A184546 Empirical: a(n) = (1/362880)*n^9 + (1/5760)*n^8 + (289/60480)*n^7 + (217/2880)*n^6 + (12949/17280)*n^5 + (28049/5760)*n^4 + (468401/22680)*n^3 + (210319/1440)*n^2 + (145955/504)*n + 77.
%F A184546 Conjectures from _Colin Barker_, Apr 14 2018: (Start)
%F A184546 G.f.: x*(539 - 3877*x + 12586*x^2 - 23898*x^3 + 29072*x^4 - 23429*x^5 + 12502*x^6 - 4270*x^7 + 853*x^8 - 77*x^9) / (1 - x)^10.
%F A184546 a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
%F A184546 (End)
%e A184546 Some solutions for 4 X 9:
%e A184546 ..0..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0..0
%e A184546 ..0..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..1..1
%e A184546 ..0..0..0..0..0..0..0..0..0....0..0..1..1..1..1..1..0..1
%e A184546 ..1..1..1..1..1..1..1..1..1....0..0..1..1..1..1..1..1..0
%Y A184546 Cf. A184548.
%K A184546 nonn
%O A184546 1,1
%A A184546 _R. H. Hardin_, Jan 16 2011