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Number of (n+3) X 5 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.
1

%I #8 Jun 02 2018 14:17:56

%S 83521,113856,153874,206145,273683,359970,468980,605203,773669,979972,

%T 1230294,1531429,1890807,2316518,2817336,3402743,4082953,4868936,

%U 5772442,6806025,7983067,9317802,10825340,12521691,14423789,16549516,18917726

%N Number of (n+3) X 5 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.

%C Column 2 of A202939.

%H R. H. Hardin, <a href="/A202933/b202933.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/5)*n^5 + (31/2)*n^4 + (781/3)*n^3 + 2874*n^2 + (589559/30)*n + 60719.

%F Conjectures from _Colin Barker_, Jun 02 2018: (Start)

%F G.f.: x*(83521 - 387270*x + 723553*x^2 - 679679*x^3 + 320618*x^4 - 60719*x^5) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=3:

%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0

%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0

%e ..0..1..1..1..0....1..1..1..1..1....0..1..1..0..1....0..1..0..1..0

%e ..0..1..0..0..0....0..1..0..0..1....0..0..1..0..1....0..1..1..0..1

%e ..1..1..1..1..1....0..0..0..1..0....0..0..1..0..1....0..0..0..0..0

%e ..0..1..0..1..0....0..0..1..1..0....0..0..1..1..0....0..1..1..1..0

%Y Cf. A202939.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2011