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A184544 Number of (n+2) X 7 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

%I A184544 #11 Apr 13 2018 11:01:08
%S A184544 309,792,1627,3024,5313,8989,14767,23648,36997,56634,84939,124972,
%T A184544 180609,256695,359215,495484,674357,906460,1204443,1583256,2060449,
%U A184544 2656497,3395151,4303816,5413957,6761534,8387467,10338132,12665889,15429643
%N A184544 Number of (n+2) X 7 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
%C A184544 Column 5 of A184548.
%H A184544 R. H. Hardin, <a href="/A184544/b184544.txt">Table of n, a(n) for n = 1..200</a>
%F A184544 Empirical: a(n) = (1/5040)*n^7 + (1/120)*n^6 + (53/360)*n^5 + (17/12)*n^4 + (5767/720)*n^3 + (3063/40)*n^2 + (11959/70)*n + 52.
%F A184544 Conjectures from _Colin Barker_, Apr 13 2018: (Start)
%F A184544 G.f.: x*(309 - 1680*x + 3943*x^2 - 5120*x^3 + 3955*x^4 - 1819*x^5 + 465*x^6 - 52*x^7) / (1 - x)^8.
%F A184544 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>8.
%F A184544 (End)
%e A184544 Some solutions for 4 X 7:
%e A184544 ..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..1..1..1..1..1
%e A184544 ..0..0..0..0..0..0..1....0..0..0..0..0..1..1....1..1..1..1..1..1..1
%e A184544 ..0..0..0..0..0..1..1....0..0..1..1..1..0..0....1..1..1..1..1..1..1
%e A184544 ..0..0..0..1..1..1..0....1..1..1..1..1..1..1....1..1..1..1..1..1..1
%Y A184544 Cf. A184548.
%K A184544 nonn
%O A184544 1,1
%A A184544 _R. H. Hardin_, Jan 16 2011