cp's OEIS Frontend

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

%I A327397 #28 May 01 2020 02:57:12
%S A327397 0,0,1,1,1,3,3,7,11,19,31,63,105,201,367,695,1285,2451,4599,8775,
%T A327397 16651,31837,60787,116639,223697,430395,828525,1598227,3085465,
%U A327397 5965999,11545611,22370999,43383571,84217615,163617805,318150719,619094385,1205614053,2349384031
%N A327397 Number of n-bead necklace structures with beads of exactly three colors and no adjacent beads having the same color.
%C A327397 Colors may be permuted without changing the necklace structure.
%H A327397 Andrew Howroyd, <a href="/A327397/b327397.txt">Table of n, a(n) for n = 1..200</a>
%F A327397 a(n) = A306888(n) - A000035(n-1). - _Yuchun Ji_, Mar 13 2020
%e A327397 Necklace structures for n=3..8 are:
%e A327397   a(3) = 1: ABC;
%e A327397   a(4) = 1: ABAC;
%e A327397   a(5) = 1: ABABC;
%e A327397   a(6) = 3: ABABAC, ABACBC, ABCABC;
%e A327397   a(7) = 3: ABABABC, ABABCAC, ABACABC;
%e A327397   a(8) = 7: ABABABAC, ABABACAC, ABABACBC, ABABCABC, ABABCBAC, ABACABAC, ABACBABC.
%Y A327397 Column k=3 of A327396.
%Y A327397 Cf. A056296, A306888, A328130.
%K A327397 nonn
%O A327397 1,6
%A A327397 _Andrew Howroyd_, Oct 04 2019
%E A327397 Terms a(33) and beyond from _Andrew Howroyd_, Oct 09 2019