login
A166328
Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
1
1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236190, 708552, 2125608, 6376680, 19129608, 57387528, 172158696, 516464424, 1549358280, 4647969864, 13943594664, 41829839238, 125486683524, 376451548188, 1129329137988
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003946, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^11 - 2*t^10 - 2*t^9 - 2*t^8 - 2*t^7 - 2*t^6 - 2*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^11)/(1-3*t+5*t^11-3*t^12), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 12 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^11)/(1-3*t+5*t^11-3*t^12), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{11, 3, -2}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 12 2020 *)
PROG
(Sage)
def A166328_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^11)/(1-3*t+5*t^11-3*t^12) ).list()
A166328_list(30) # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A164697 A165184 A165756 * A166468 A166858 A167105
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved