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A166225 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747903999999180, 429916159999934400, 17196646399996064820, 687865855999790145600, 27514634239989507936000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170760, 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 (39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
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)/(780*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-40*t+819*t^10-780*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-40*t+819*t^10-780*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 07 2016 *)
coxG[{10, 780, -39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 30 2018 *)
PROG
(Sage)
def A166225_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-40*t+819*t^10-780*t^11) ).list()
A166225_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164685 A165173 A165692 * A166435 A166714 A167094
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved

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Last modified July 21 02:16 EDT 2024. Contains 374462 sequences. (Running on oeis4.)