A262415 - OEIS

%I #8 Dec 31 2018 11:26:33

%S 6,45,270,1701,10206,61965,371790,2237301,13423806,80601885,483611310,

%T 2902199301,17413195806,104483957805,626903746830,3761465527701,

%U 22568793166206,135413146417725,812478878506350,4874876757822501

%N Number of (n+1) X (3+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

%H R. H. Hardin, <a href="/A262415/b262415.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) + 9*a(n-2) - 54*a(n-3).

%F Conjectures from _Colin Barker_, Dec 31 2018: (Start)

%F G.f.: 3*x*(2 + 3*x - 18*x^2) /  ((1 - 3*x)*(1 + 3*x)*(1 - 6*x)).

%F a(n) = 3^(n-1) * (2^(n+3) - 2) / 2 for n even.

%F a(n) = 3^(n-1) * (2^(n+3) - 4) / 2 for n odd.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 3 of A262420.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 22 2015