A002075 Number of equivalence classes with primitive period n of base 3 necklaces, where necklaces are equivalent under rotation and permutation of symbols.

1, 1, 2, 4, 8, 22, 52, 140, 366, 992, 2684, 7404, 20440, 56992, 159440, 448540, 1266080, 3587610, 10195276, 29057520, 83018728, 237737984, 682196948, 1961323740, 5648590728, 16294032160, 47071589778, 136171440600

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

References

• N. J. Fine, Classes of periodic sequences, Illinois J. Math., 2 (1958), 285-302.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Index entries for sequences related to necklaces

Crossrefs

Cf. A000013, A000048, A002076.

Formula

Reference gives formula.

Sequence A002076 can be found as follows: Let F3(n) = this sequence, F3*(n) = function from A002076. Then F3*(n) = Sum_{ d divides n } F3(d).

Extensions

Better description and more terms from Mark Weston (mweston(AT)uvic.ca), Oct 07 2001