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%I #9 Jun 03 2018 07:57:30
%S 130321,206145,330853,533832,857408,1360328,2121734,3245653,4866027,
%T 7152307,10315635,14615638,20367858,27951842,37819916,50506667,
%U 66639157,86947893,112278577,143604660,182040724,228856716,285493058,353576657
%N Number of (n+3) X 7 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.
%C Column 4 of A202939.
%H R. H. Hardin, <a href="/A202935/b202935.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/210)*n^7 + (11/20)*n^6 + (81/5)*n^5 + (1713/8)*n^4 + (90179/60)*n^3 + (337713/40)*n^2 + (15214631/420)*n + 83919.
%F Conjectures from _Colin Barker_, Jun 03 2018: (Start)
%F G.f.: x*(130321 - 836423*x + 2330681*x^2 - 3638908*x^3 + 3428986*x^4 - 1947234*x^5 + 616520*x^6 - 83919*x^7) / (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>8.
%F (End)
%e Some solutions for n=1:
%e ..0..0..0..0..1..1..1....0..0..0..1..0..0..0....0..0..0..1..1..0..1
%e ..0..0..0..1..0..0..0....0..0..0..0..1..0..1....0..0..0..1..1..0..0
%e ..0..0..0..0..0..0..1....0..0..0..1..0..0..0....0..0..0..1..0..1..1
%e ..0..0..1..1..1..1..1....0..1..1..1..1..1..1....0..0..0..0..0..1..0
%Y Cf. A202939.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 26 2011
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