A328130 Number of n-bead necklace structures with beads of exactly four colors and no adjacent beads having the same color.

0, 0, 0, 1, 1, 5, 10, 33, 83, 237, 640, 1817, 5005, 14099, 39504, 111585, 315235, 894845, 2544220, 7256607, 20738097, 59405343, 170488450, 490221899, 1411923987, 4073098085, 11767069378, 34041318969, 98603778565, 285954140473, 830194632190, 2412764894021, 7018972487319

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=4..7 are:
a(4) = 1: ABCD;
a(5) = 1: ABACD;
a(6) = 5: ABABCD, ABACAD, ABACBD, ABACDC, ABCABD;
a(7) = 10: ABABACD, ABABCAD, ABABCBD, ABABCDC, ABACABD, ABACADC, ABACBCD, ABACBDC, ABACDBC, ABCABCD.
		

Links

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

Crossrefs

Column k=4 of A327396.

Cf. A056297, A309673, A327397.

Extensions

Terms a(24) and beyond from Andrew Howroyd, Oct 09 2019