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%I #9 May 31 2018 11:10:38
%S 1331,2835,5735,10918,19614,33468,54618,85779,130333,192425,277065,
%T 390236,539008,731658,977796,1288497,1676439,2156047,2743643,3457602,
%U 4318514,5349352,6575646,8025663,9730593,11724741,14045725,16734680
%N Number of (n+2) X 6 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.
%C Column 4 of A202461.
%H R. H. Hardin, <a href="/A202457/b202457.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/120)*n^6 + (17/40)*n^5 + (27/4)*n^4 + (1195/24)*n^3 + (22769/120)*n^2 + (28277/60)*n + 613.
%F Conjectures from _Colin Barker_, May 31 2018: (Start)
%F G.f.: x*(1331 - 6482*x + 13841*x^2 - 16277*x^3 + 10983*x^4 - 4003*x^5 + 613*x^6) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=5:
%e ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..1..0..0
%e ..0..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..0..0....0..0..0..1..0..0
%e ..0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..1..0....0..0..0..1..0..0
%e ..0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..1..0....0..0..0..1..1..0
%e ..0..0..0..1..0..1....0..0..0..0..1..1....0..0..0..1..1..0....0..0..0..1..1..1
%e ..0..0..0..0..1..0....0..0..0..0..1..1....0..0..0..1..1..0....0..0..0..1..1..1
%e ..0..0..1..1..1..1....0..1..1..1..1..1....0..0..0..0..1..0....0..0..1..1..1..1
%Y Cf. A202461.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 19 2011
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