A334625 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,1

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)

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)

CROSSREFS