OFFSET
2,1
REFERENCES
P. Renteln, The distance spectra of Cayley graphs of Coxeter groups, Discrete Math., 311 (2011), 738-755.
LINKS
B. Foster-Greenwood, C. Kriloff, Spectra of Cayley Graphs of Complex Reflection Groups, arXiv preprint arXiv:1502.07392, 2015
FORMULA
a(n)=Sum_{w in W(D_n)} l_T(w)=|W(D_n)|Sum_{i=1}^n (d_i-1)/d_i=2^(n-1)*n!*(1/2+3/4+...+(2n-3)/(2n-2)+(n-1)/n) where T=all reflections in W(D_n), l_T(1)=0 and otherwise l_T(w)=min{k|w=t_1*...*t_k for t_i in T}, and d_1,...,d_n are the degrees of W(D_n)
EXAMPLE
a(3)=46 because W(D_3)=W(A_3) and in sequence A067318, a(3)=46.
MAPLE
seq(2^(n-1)*factorial(n)*(add((2*k-1)/(2*k), k=1..n-1)+(n-1)/n), n=2..100);
MATHEMATICA
Table[2^(n-1)*Factorial[n]*(Sum[(2*k-1)/(2*k), {k, 1, n-1}]+(n-1)/n), {n, 2, 100}]
PROG
(Sage)
[2^(n-1)*factorial(n)*(sum([(2*k-1)/(2*k) for k in [1..n-1]])+(n-1)/n) for n in [2..100]]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cathy Kriloff, Oct 10 2011
STATUS
approved