A183877 - OEIS

%I #17 Sep 30 2018 20:22:52

%S 1,31,171,631,2059,6399,19483,58807,176859,531103,1593931,4782519,

%T 14348395,43046143,129139515,387419767,1162260667,3486783519,

%U 10460352235,31381058551,94143177675,282429535231,847288608091,2541865826871

%N Number of arrangements of n+2 numbers in 0..2 with each number being the sum mod 3 of two others.

%H R. H. Hardin, <a href="/A183877/b183877.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical (for n>=2): 3^(n+2) - 2*(n+3)^2. - _Vaclav Kotesovec_, Nov 27 2012

%F Conjectures from _Colin Barker_, Apr 05 2018: (Start)

%F G.f.: x*(1 + 25*x - 3*x^2 - 33*x^3 + 18*x^4) / ((1 - x)^3*(1 - 3*x)).

%F a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4) for n>5.

%F (End)

%F Conjecture is true. The complement consists of arrangements of the forms

%F 1*, 2*, 01*, 02*, 10*, 12*, 20*, 21*, 001*, 002* and 120*. _Robert Israel_, Sep 30 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%p 1, seq(3^(n+2)-2*(n+3)^2, n=2..30); # _Robert Israel_, Sep 30 2018

%Y Column 2 of A183884.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 07 2011