%I #9 Jun 03 2018 07:57:36
%S 160000,273683,481798,857408,1515902,2631416,4457228,7350643,11802908,
%T 18474721,28237922,42223978,61879898,89032238,125959880,175476293,
%U 241022008,326768063,437731198,579901604,760384054,987553268,1271224388
%N Number of (n+3) X 8 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.
%C Column 5 of A202939.
%H R. H. Hardin, <a href="/A202936/b202936.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/1680)*n^8 + (17/210)*n^7 + (134/45)*n^6 + (256/5)*n^5 + (352481/720)*n^4 + (55381/20)*n^3 + (32201731/2520)*n^2 + (19670981/420)*n + 97073.
%F Conjectures from _Colin Barker_, Jun 03 2018: (Start)
%F G.f.: x*(160000 - 1166317*x + 3778651*x^2 - 7066186*x^3 + 8314586*x^4 - 6291988*x^5 + 2987174*x^6 - 812969*x^7 + 97073*x^8) / (1 - x)^9.
%F 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 (End)
%e Some solutions for n=1:
%e ..0..0..0..0..0..1..1..1....0..0..0..0..1..0..0..1....0..0..0..0..0..0..0..0
%e ..0..0..0..0..1..1..0..0....0..0..0..0..1..1..1..0....0..0..0..0..0..0..0..1
%e ..0..0..0..0..0..1..1..1....0..0..0..0..1..0..0..0....0..0..0..0..0..1..1..1
%e ..0..0..0..0..1..0..0..1....0..0..0..0..0..0..0..0....0..0..0..0..0..0..1..0
%Y Cf. A202939.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 26 2011