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A202332 Number of (n+1) X 6 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

%I A202332 #8 May 28 2018 08:02:29
%S A202332 64,191,478,1052,2102,3896,6800,11299,18020,27757,41498,60454,86090,
%T A202332 120158,164732,222245,295528,387851,502966,645152,819262,1030772,
%U A202332 1285832,1591319,1954892,2385049,2891186,3483658,4173842,4974202,5898356,6961145
%N A202332 Number of (n+1) X 6 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
%C A202332 Column 5 of A202335.
%H A202332 R. H. Hardin, <a href="/A202332/b202332.txt">Table of n, a(n) for n = 1..210</a>
%F A202332 Empirical: a(n) = (1/360)*n^6 + (1/12)*n^5 + (17/18)*n^4 + (16/3)*n^3 + (5779/360)*n^2 + (295/12)*n + 17.
%F A202332 Conjectures from _Colin Barker_, May 28 2018: (Start)
%F A202332 G.f.: x*(64 - 257*x + 485*x^2 - 523*x^3 + 331*x^4 - 115*x^5 + 17*x^6) / (1 - x)^7.
%F A202332 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 A202332 (End)
%e A202332 Some solutions for n=5:
%e A202332 ..0..0..0..1..1..1....0..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..1..0
%e A202332 ..1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..1..0
%e A202332 ..1..1..1..1..1..1....0..0..0..0..0..1....0..0..0..1..1..1....0..0..0..0..1..1
%e A202332 ..1..1..1..1..1..1....0..0..0..0..0..1....1..1..1..1..1..1....0..0..0..0..1..1
%e A202332 ..1..1..1..1..1..1....0..0..0..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
%e A202332 ..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....0..0..1..1..1..1
%Y A202332 Cf. A202335.
%K A202332 nonn
%O A202332 1,1
%A A202332 _R. H. Hardin_, Dec 17 2011