A327397 - OEIS

%I #28 May 01 2020 02:57:12

%S 0,0,1,1,1,3,3,7,11,19,31,63,105,201,367,695,1285,2451,4599,8775,

%T 16651,31837,60787,116639,223697,430395,828525,1598227,3085465,

%U 5965999,11545611,22370999,43383571,84217615,163617805,318150719,619094385,1205614053,2349384031

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

%C Colors may be permuted without changing the necklace structure.

%H Andrew Howroyd, <a href="/A327397/b327397.txt">Table of n, a(n) for n = 1..200</a>

%F a(n) = A306888(n) - A000035(n-1). - _Yuchun Ji_, Mar 13 2020

%e Necklace structures for n=3..8 are:

%e   a(3) = 1: ABC;

%e   a(4) = 1: ABAC;

%e   a(5) = 1: ABABC;

%e   a(6) = 3: ABABAC, ABACBC, ABCABC;

%e   a(7) = 3: ABABABC, ABABCAC, ABACABC;

%e   a(8) = 7: ABABABAC, ABABACAC, ABABACBC, ABABCABC, ABABCBAC, ABACABAC, ABACBABC.

%Y Column k=3 of A327396.

%Y Cf. A056296, A306888, A328130.

%K nonn

%O 1,6

%A _Andrew Howroyd_, Oct 04 2019

%E Terms a(33) and beyond from _Andrew Howroyd_, Oct 09 2019