A274018 Number of n-bead ternary necklaces (no turning over allowed) that avoid the subsequence 110.

1, 3, 6, 10, 21, 42, 103, 237, 603, 1519, 3942, 10257, 27131, 71940, 192462, 516933, 1395636, 3781356, 10283911, 28050600, 76732047, 210414811, 578330649, 1592821005, 4395261552, 12149386569, 33637309323, 93267459520, 258961863288, 719938597227, 2003881480452, 5583818718102, 15575529493713

Offset

0,2

Comments

The pattern in this enumeration must be contiguous (all three values next to each other in one sequence of three letters).

Links

Table of n, a(n) for n=0..32.

Math Stackexchange, Marko Riedel et al., Counting circular sequences.

Marko Riedel, Maple code for this sequence.

Formula

G.f.: 1 - Sum_{n>=1} (phi(n)/n)*log(x^(3*n) - q*x^n + 1), where q=3 is the number of symbols in the alphabet we are using. - Petros Hadjicostas, Sep 12 2017

a(n) = (1/n)*Sum_{d|n} phi(n/d)*A215885(d) for n >= 1. - Petros Hadjicostas, Sep 13 2017

Example

The necklace
    1--1
   /    \
  0      0
  |      |
  1      2
   \    /
    0--0
contains one instance of the subsequence starting in the upper left corner. Unlike a bracelet, the necklace is oriented.

Crossrefs

Cf. A000031, A274017, A274019, A274020.

Sequence in context: A061883 A027671 A167617 * A068149 A068709 A068804

Adjacent sequences: A274015 A274016 A274017 * A274019 A274020 A274021

Keyword

nonn

Author

Marko Riedel, Jun 06 2016

Status

approved