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, 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

G. C. Greubel, Table of n, a(n) for n = 0..500

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

Adjacent sequences: A166164 A166165 A166166 * A166168 A166169 A166170

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved