A334625 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.
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, 27, 27, 30, 30, 33, 33, 33, 33, 36, 36, 39, 39, 39, 39, 42, 42, 45, 45, 45, 45, 48, 48, 51, 51, 51, 51, 54, 54, 57, 57, 57, 57, 60, 60
Offset: 3
Keywords
Links
- Fausto A. C. Cariboni, Table of n, a(n) for n = 3..111
- Fausto A. C. Cariboni, Examples of cyclic arrangements for a(3)-a(111)
Crossrefs
Cf. A336351.
Formula
Conjectures from Colin Barker, Sep 10 2020: (Start)
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)).
a(n) = a(n-1) + a(n-6) - a(n-7) for n>15.
(End)
Comments