A239024 - OEIS

%I #9 Oct 25 2018 05:48:07

%S 1,3,4,11,16,43,64,171,256,683,1024,2731,4096,10923,16384,43691,65536,

%T 174763,262144,699051,1048576,2796203,4194304,11184811,16777216,

%U 44739243,67108864,178956971,268435456,715827883,1073741824,2863311531,4294967296

%N Number of n X 2 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

%H R. H. Hardin, <a href="/A239024/b239024.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-2) - 4*a(n-4).

%F Conjectures from _Colin Barker_, Oct 25 2018: (Start)

%F G.f.: x*(1 + 3*x - x^2 - 4*x^3) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)).

%F a(n) = (2 + (-2)^n + 2*(-1)^n + 7*2^n) / 12.

%F (End)

%e Some solutions for n=5:

%e ..2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0

%e ..1..0....2..0....2..0....2..0....1..2....1..0....1..0....2..0....2..0....1..0

%e ..2..0....1..2....1..0....1..2....2..1....2..0....2..0....1..2....1..2....2..0

%e ..2..0....2..1....1..0....1..2....1..0....1..0....1..2....2..1....1..2....2..0

%e ..1..2....1..2....2..0....2..1....2..0....2..0....2..1....1..0....2..0....1..0

%Y Column 2 of A239030.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 09 2014