A327397 Number of n-bead necklace structures with beads of exactly three colors and no adjacent beads having the same color.

0, 0, 1, 1, 1, 3, 3, 7, 11, 19, 31, 63, 105, 201, 367, 695, 1285, 2451, 4599, 8775, 16651, 31837, 60787, 116639, 223697, 430395, 828525, 1598227, 3085465, 5965999, 11545611, 22370999, 43383571, 84217615, 163617805, 318150719, 619094385, 1205614053, 2349384031

Offset

1,6

Comments

Colors may be permuted without changing the necklace structure.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Formula

a(n) = A306888(n) - A000035(n-1). - Yuchun Ji, Mar 13 2020

Example

Necklace structures for n=3..8 are:
  a(3) = 1: ABC;
  a(4) = 1: ABAC;
  a(5) = 1: ABABC;
  a(6) = 3: ABABAC, ABACBC, ABCABC;
  a(7) = 3: ABABABC, ABABCAC, ABACABC;
  a(8) = 7: ABABABAC, ABABACAC, ABABACBC, ABABCABC, ABABCBAC, ABACABAC, ABACBABC.

Crossrefs

Column k=3 of A327396.

Cf. A056296, A306888, A328130.

Sequence in context: A358827 A022403 A082550 * A036056 A339586 A278789

Adjacent sequences: A327394 A327395 A327396 * A327398 A327399 A327400

Keyword

nonn

Author

Andrew Howroyd, Oct 04 2019

Extensions

Terms a(33) and beyond from Andrew Howroyd, Oct 09 2019

Status

approved