OFFSET
0,5
COMMENTS
Taking the overlay of the two generating functions in the bisections A072844 and A072266, shows that a(n) = A094052(n-1), n>0. - R. J. Mathar, Nov 05 2024
LINKS
Sean A. Irvine, Table of n, a(n) for n = 0..1000
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 134.
Haggai Liu, Enumerative Properties of Cogrowth Series on Free Products of Finite Groups, ACA 2021 Session on Algorithmic Combinatorics, 2021.
Sean A. Irvine, Java program (github)
FORMULA
G.f.: F_7(x) where F_n(x) = 1/2 + (1/(2*n)) * Sum_{j=0..n-1} 1 / (1 - 2*cos(2*Pi*j/n)*x).
EXAMPLE
a(4) = 3 corresponds to the TTTT = TSTS = STST = 1. Note: TSTS = (TSTS)(TT) = T(STST)T = TT = 1.
a(9) = 9 corresponds to the words SSSSSSSTT = SSSSSSTTS = SSSSSTTSS = SSSSTTSSS = SSSTTSSSS = SSTTSSSSS = STTSSSSSS = TTSSSSSSS = TSSSSSSST = 1.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sean A. Irvine, Nov 01 2024
STATUS
approved