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A202334 Number of (n+1) X 8 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

%I A202334 #10 May 28 2018 08:41:58
%S A202334 100,368,1112,2906,6800,14588,29174,55057,98958,170614,283766,457370,
%T A202334 717062,1096910,1641488,2408309,3470656,4920852,6874012,9472322,
%U A202334 12889892,17338232,23072402,30397889,39678266,51343690,65900298,83940562
%N A202334 Number of (n+1) X 8 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
%C A202334 Column 7 of A202335.
%H A202334 R. H. Hardin, <a href="/A202334/b202334.txt">Table of n, a(n) for n = 1..210</a>
%F A202334 Empirical: a(n) = (1/20160)*n^8 + (1/420)*n^7 + (67/1440)*n^6 + (59/120)*n^5 + (8927/2880)*n^4 + (1439/120)*n^3 + (140383/5040)*n^2 + (1243/35)*n + 21.
%F A202334 Conjectures from _Colin Barker_, May 28 2018: (Start)
%F A202334 G.f.: x*(100 - 532*x + 1400*x^2 - 2254*x^3 + 2366*x^4 - 1636*x^5 + 722*x^6 - 185*x^7 + 21*x^8) / (1 - x)^9.
%F A202334 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 A202334 (End)
%e A202334 Some solutions for n=5:
%e A202334   0 0 0 0 0 0 0 0    0 0 0 0 0 0 0 1    0 0 0 0 0 0 0 0
%e A202334   0 0 0 0 0 0 0 1    0 0 0 0 0 0 1 1    0 0 0 0 0 0 1 1
%e A202334   0 0 0 0 0 0 1 1    0 0 0 0 0 1 1 1    0 0 0 0 0 0 1 1
%e A202334   0 0 0 0 0 0 1 1    0 0 0 0 0 1 1 1    0 0 1 1 1 1 1 1
%e A202334   0 0 1 1 1 1 1 1    1 1 1 1 1 1 1 1    1 1 1 1 1 1 1 1
%e A202334   1 1 1 1 1 1 1 1    0 0 1 1 1 1 1 1    1 1 1 1 1 1 1 1
%Y A202334 Cf. A202335.
%K A202334 nonn
%O A202334 1,1
%A A202334 _R. H. Hardin_, Dec 17 2011