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A166230
Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244545501, 563751691026330240, 23113819332078093360, 947666592615142522080, 38854330297218411872400
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170761, 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 (40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
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)/(820*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 07 2016 *)
coxG[{10, 820, -40}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)
PROG
(Sage)
def A166230_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11) ).list()
A166230_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164686 A165174 A165693 * A166436 A166716 A167095
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved