%I #17 Sep 25 2020 04:31:04

%S 3,3,3,3,3,3,9,9,9,9,12,12,15,15,15,15,18,18,21,21,21,21,24,24,27,27,

%T 27,27,30,30,33,33,33,33,36,36,39,39,39,39,42,42,45,45,45,45,48,48,51,

%U 51,51,51,54,54,57,57,57,57,60,60

%N Maximal size of a subset T of S = {1,2,...,n} with a cyclic arrangement of T such that any three neighbors can be reordered in an arithmetic progression.

%H Fausto A. C. Cariboni, <a href="/A334625/b334625.txt">Table of n, a(n) for n = 3..111</a>

%H Fausto A. C. Cariboni, <a href="/A334625/a334625.txt">Examples of cyclic arrangements for a(3)-a(111)</a>

%F Conjectures from _Colin Barker_, Sep 10 2020: (Start)

%F G.f.: 3*x^3*(1 + x^6 + x^10 - x^12) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)).

%F a(n) = a(n-1) + a(n-6) - a(n-7) for n>15.

%F (End)

%Y Cf. A336351.

%K nonn

%O 3,1

%A _Fausto A. C. Cariboni_, Sep 09 2020