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A262327 Number of (n+1) X (3+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 A262327 #7 Dec 31 2018 06:08:25
%S A262327 6,15,90,351,2106,10935,65610,378351,2270106,13482855,80897130,
%T A262327 484142751,2904856506,17417978775,104507872650,626946793551,
%U A262327 3761680761306,22569180586695,135415083520170,812482365290751,4874894191744506
%N A262327 Number of (n+1) X (3+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.
%H A262327 R. H. Hardin, <a href="/A262327/b262327.txt">Table of n, a(n) for n = 1..210</a>
%F A262327 Empirical: a(n) = 6*a(n-1) + 9*a(n-2) - 54*a(n-3).
%F A262327 Conjectures from _Colin Barker_, Dec 31 2018: (Start)
%F A262327 G.f.: 3*x*(2 - 7*x - 18*x^2) / ((1 - 3*x)*(1 + 3*x)*(1 - 6*x)).
%F A262327 a(n) = 3^(n-2)*(14 + 2^(2+n)) / 2 for n even.
%F A262327 a(n) = 3^(n-2)*(28 + 2^(2+n)) / 2 for n odd.
%F A262327 (End)
%e A262327 Some solutions for n=4:
%e A262327 ..0..0..0..0....0..1..1..0....1..0..0..1....0..0..1..1....1..1..1..1
%e A262327 ..0..0..0..0....0..1..1..0....1..1..1..1....0..0..1..1....0..0..0..0
%e A262327 ..0..0..0..0....0..0..0..0....0..1..1..0....1..0..0..1....1..1..0..0
%e A262327 ..1..0..0..1....1..0..0..1....1..0..0..1....1..1..1..1....0..0..1..1
%e A262327 ..1..0..0..1....1..0..0..1....1..0..0..1....0..1..1..0....1..1..0..0
%Y A262327 Column 3 of A262332.
%K A262327 nonn
%O A262327 1,1
%A A262327 _R. H. Hardin_, Sep 18 2015