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A184680 Number of (n+1) X 4 binary arrays with every 2 X 2 subblock singular.

%I A184680 #11 Jul 22 2025 09:40:59
%S A184680 76,544,3360,21968,140816,909520,5858896,37779664,243525712,
%T A184680 1569965008,10120785744,65244856016,420606054992,2711476238800,
%U A184680 17479769838928,112684908266704,726433311008848,4683017326649296,30189489673849680
%N A184680 Number of (n+1) X 4 binary arrays with every 2 X 2 subblock singular.
%C A184680 Column 3 of A184686.
%H A184680 R. H. Hardin, <a href="/A184680/b184680.txt">Table of n, a(n) for n = 1..200</a>
%F A184680 Empirical: a(n) = 7*a(n-1) + 2*a(n-2) - 40*a(n-3) + 24*a(n-4) + 16*a(n-5).
%F A184680 Empirical g.f.: 4*x*(19 + 3*x - 150*x^2 + 100*x^3 + 64*x^4) / ((1 - 2*x)*(1 - 5*x - 12*x^2 + 16*x^3 + 8*x^4)). - _Colin Barker_, Apr 14 2018
%e A184680 Some solutions for 3 X 4:
%e A184680 ..0..0..0..0....0..0..0..0....1..0..1..0....0..0..0..0....0..0..1..0
%e A184680 ..1..1..0..0....1..0..0..0....0..0..0..0....0..1..0..0....0..0..0..0
%e A184680 ..1..1..0..1....0..0..1..1....0..0..0..0....0..1..0..0....0..1..0..0
%Y A184680 Cf. A184686.
%K A184680 nonn
%O A184680 1,1
%A A184680 _R. H. Hardin_, Jan 19 2011