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A166258
Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777926690, 1223881242228730800, 53850774658062239550, 2369434084954654251600, 104255099738001078372000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170764, 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 (43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
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)/(946*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-44*t+989*t^10-946*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-44*t+989*t^10-946*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 08 2016 *)
coxG[{10, 946, -43}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)
PROG
(Sage)
def A166258_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-44*t+989*t^10-946*t^11) ).list()
A166258_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164690 A165177 A165699 * A166439 A166738 A167098
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved