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

Author

Andrew Howroyd, Oct 04 2019

Keywords

• nonn

Comments

Colors may be permuted without changing the necklace structure.

Examples

			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.
		

Links

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

Crossrefs

Column k=3 of A327396.

Cf. A056296, A306888, A328130.

Formula

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

Extensions

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