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A166313
Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708931688, 2524758347319736320, 118663642324025116416, 5577191189229063412224, 262127985893760478586112
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170767, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (46,46,46,46,46,46,46,46,46,-1081).
FORMULA
G.f.: (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)/(1081*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{10, 1081, -46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 05 2017 *)
PROG
(Sage)
def A166313_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11) ).list()
A166313_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164693 A165180 A165708 * A166442 A166854 A167101
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved