A397015 - OEIS

A397015

Number of distinct sequences of reversible necklaces that can be obtained by replacing n white beads with black beads, one bead at a time.

1, 1, 1, 2, 4, 14, 57, 347, 2275, 20752, 200805, 2239376, 28097136, 381963696, 5582142632, 87829124289, 1478237810536, 26151806259633, 491527066667949, 9640606422165480, 200405171905030878, 4317192207291540985, 97857028247700646166, 2302633887346258478720

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OFFSET

1,4

COMMENTS

This is a shape-only variation of A003322. A003322 is higher at n=9, 12, 15, 16, ... because it counts distinct beads chosen to be replaced, and it is possible for distinct beads to result in the same necklace. For example, BBWBWWBWW has 5 distinct white beads but only 4 resulting necklaces; replacing the 2nd white bead creates BBWBBWBWW, whereas replacing the 4th white bead creates BBWBWWBBW which is equivalent after rotation.

LINKS

Martin Fuller, Table of n, a(n) for n = 1..35

CROSSREFS

Cf. A003322.

Sequence in context: A006384 A059687 A204198 * A003322 A170939 A030952

Adjacent sequences: A397012 A397013 A397014 * A397016 A397017 A397018

KEYWORD

nonn

AUTHOR

Martin Fuller and D. S. McNeil, Jun 13 2026

STATUS

approved