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

3,1

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

Cf. A336351.

Sequence in context: A351836 A105159 A365458 * A209291 A332875 A176873

Adjacent sequences: A334622 A334623 A334624 * A334626 A334627 A334628

Keyword

nonn

Author

Fausto A. C. Cariboni, Sep 09 2020

Status

approved