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A166167
Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575872, 3757718396730726, 135277862282282160, 4870003042161295290, 175320109517775581520, 6311523942638803173600
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170756, 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 (35,35,35,35,35,35,35,35,35,-630).
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)/(630*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 06 2016 *)
coxG[{630, 10, -35}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)
PROG
(Sage)
def A166167_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11) ).list()
A166167_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164673 A165169 A165654 * A166431 A166689 A167090
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved