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A183885 Number of arrangements of n+3 numbers in 0..2 with each number being the sum mod 3 of three others. 1

%I #12 Apr 05 2018 09:51:47

%S 1,121,631,2059,6399,19483,58807,176859,531103,1593931,4782519,

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

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

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

%C Column 2 of A183892.

%H R. H. Hardin, <a href="/A183885/b183885.txt">Table of n, a(n) for n = 1..62</a>

%F Empirical (for n>=3): 3^(n+3) - 2*(n+4)^2. - _Vaclav Kotesovec_, Nov 27 2012

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

%F G.f.: x*(1 + 115*x - 83*x^2 - 285*x^3 + 410*x^4 - 150*x^5) / ((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>6.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

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

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

%Y Cf. A183892.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 07 2011

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Last modified April 24 03:00 EDT 2024. Contains 371917 sequences. (Running on oeis4.)