%I #10 May 31 2018 14:06:42
%S 2197,5854,14586,33468,71088,141192,264822,473031,810265,1338508,
%T 2142292,3334680,5064336,7523802,10959108,15680847,22076853,30626626,
%U 41917654,56663788,75725832,100134516,131116026,170120271,218852073,279305472
%N Number of (n+2) X 8 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.
%C Column 6 of A202461.
%H R. H. Hardin, <a href="/A202459/b202459.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/6720)*n^8 + (19/1680)*n^7 + (431/1440)*n^6 + (193/48)*n^5 + (90001/2880)*n^4 + (5873/40)*n^3 + (2076229/5040)*n^2 + (10915/14)*n + 823.
%F Conjectures from _Colin Barker_, May 31 2018: (Start)
%F G.f.: x*(2197 - 13919*x + 40992*x^2 - 71610*x^3 + 80058*x^4 - 58194*x^5 + 26730*x^6 - 7071*x^7 + 823*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=4:
%e ..0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0
%e ..0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..1
%e ..0..0..0..0..0..1..1..1....0..0..0..0..0..1..0..0....0..0..0..0..0..1..1..1
%e ..0..0..0..0..0..1..1..1....0..0..0..0..0..1..1..0....0..0..0..0..1..1..1..1
%e ..0..1..1..1..1..1..1..1....0..0..0..0..1..1..1..1....0..0..1..1..1..1..1..1
%e ..0..0..0..0..1..1..1..1....0..0..0..0..0..1..1..1....0..0..0..0..0..1..1..1
%Y Cf. A202461.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 19 2011
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