%I #8 May 28 2018 08:02:29

%S 64,191,478,1052,2102,3896,6800,11299,18020,27757,41498,60454,86090,

%T 120158,164732,222245,295528,387851,502966,645152,819262,1030772,

%U 1285832,1591319,1954892,2385049,2891186,3483658,4173842,4974202,5898356,6961145

%N 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 Column 5 of A202335.

%H R. H. Hardin, <a href="/A202332/b202332.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Conjectures from _Colin Barker_, May 28 2018: (Start)

%F 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 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..1..1..1....0..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..1..0

%e ..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 ..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 ..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 ..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 ..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 Cf. A202335.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 17 2011