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1/32 the number of (2n+1) X 6 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.
1

%I #7 Jan 14 2017 09:38:16

%S 2016,5912192,19855042560,70577422755840,258888921984516096,

%T 968823452179344785408,3676119951496408119115776,

%U 14091184863095839321177456640,54435471052008802940182132162560

%N 1/32 the number of (2n+1) X 6 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

%C Column 5 of A183772(2n).

%H R. H. Hardin, <a href="/A183768/b183768.txt">Table of n, a(n) for n = 1..65</a>

%e Some solutions for 3 X 6:

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011