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A166165
Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992186870, 99307704726518400, 3475769665427372880, 121651938289931061600, 4257817840146642534000, 149023624405099426920000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170755, 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 (34, 34, 34, 34, 34, 34, 34, 34, 34, -595).
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)/(595*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 06 2016 *)
coxG[{595, 10, -34}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)
PROG
(Sage)
def A166165_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11) ).list()
A166165_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164672 A165168 A165651 * A166430 A166688 A167089
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved