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Number of (n+1) X 4 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
1

%I #8 May 27 2018 14:42:35

%S 36,82,162,289,478,746,1112,1597,2224,3018,4006,5217,6682,8434,10508,

%T 12941,15772,19042,22794,27073,31926,37402,43552,50429,58088,66586,

%U 75982,86337,97714,110178,123796,138637,154772,172274,191218,211681,233742

%N Number of (n+1) X 4 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

%C Column 3 of A202335.

%H R. H. Hardin, <a href="/A202330/b202330.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/12)*n^4 + (4/3)*n^3 + (83/12)*n^2 + (44/3)*n + 13.

%F Conjectures from _Colin Barker_, May 27 2018: (Start)

%F G.f.: x*(36 - 98*x + 112*x^2 - 61*x^3 + 13*x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

%F (End)

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Cf. A202335.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 17 2011