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A327397
Number of n-bead necklace structures with beads of exactly three colors and no adjacent beads having the same color.
4
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
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.
Sequence in context: A358827 A022403 A082550 * A036056 A339586 A278789
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 04 2019
EXTENSIONS
Terms a(33) and beyond from Andrew Howroyd, Oct 09 2019
STATUS
approved