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A262326 Number of (n+1) X (2+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

%I A262326 #10 Mar 20 2018 20:36:53
%S A262326 3,5,15,33,99,261,783,2241,6723,19845,59535,177633,532899,1595781,
%T A262326 4787343,14353281,43059843,129153285,387459855,1162300833,3486902499,
%U A262326 10460471301,31381413903,94143533121,282430599363,847289672325
%N A262326 Number of (n+1) X (2+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.
%C A262326 Column 2 of A262332.
%H A262326 R. H. Hardin, <a href="/A262326/b262326.txt">Table of n, a(n) for n = 1..210</a>
%F A262326 Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - 9*a(n-3).
%F A262326 Conjectures from _Colin Barker_, Mar 20 2018: (Start)
%F A262326 G.f.: x*(3 - 4*x - 9*x^2) / ((1 - 3*x)*(1 - 3*x^2)).
%F A262326 a(n) = 2*3^(n/2-1) + 3^(n-1) for n even.
%F A262326 a(n) = 2*3^((n-3)/2+1) + 3^(n-1) for n odd.
%F A262326 (End)
%e A262326 Some solutions for n=4:
%e A262326 ..0..1..1....0..0..0....0..1..1....0..0..0....1..1..0....0..0..0....1..1..0
%e A262326 ..1..1..0....1..1..0....0..1..1....0..0..0....1..1..0....1..1..0....0..0..0
%e A262326 ..0..0..0....1..1..0....1..1..0....0..0..0....0..1..1....1..1..0....1..1..0
%e A262326 ..0..1..1....0..1..1....1..1..0....1..1..0....0..1..1....1..1..0....0..0..0
%e A262326 ..1..1..0....0..1..1....0..0..0....1..1..0....0..0..0....1..1..0....1..1..0
%Y A262326 Cf. A262332.
%K A262326 nonn
%O A262326 1,1
%A A262326 _R. H. Hardin_, Sep 18 2015