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A166303
Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558592715, 1566328930136625600, 70484801856146057160, 3171816083526478304400, 142731723758687281647000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170765, 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 (44, 44, 44, 44, 44, 44, 44, 44, 44, -990).
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)/(990*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-45*t+1034*t^10-990*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-45*t+1034*t^10-990*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{10, 990, -44}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)
PROG
(Sage)
def A166303_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-45*t+1034*t^10-990*t^11)).list()
A166303_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164691 A165178 A165702 * A166440 A166739 A167099
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved