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A166145
Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746825645, 72253221392051700, 2456609527329070575, 83524723929165033900, 2839840613590816720500, 96554580862060757805600
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170754, 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 (33, 33, 33, 33, 33, 33, 33, 33, 33, -561).
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)/(561*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-34*t+594*t^10-561*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-34*t+594*t^10-561*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 27 2016 *)
coxG[{561, 10, -33}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 11 2020 *)
PROG
(Sage)
def A166145_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-34*t+594*t^10-561*t^11) ).list()
A166145_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164671 A165167 A165650 * A166429 A166683 A167088
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved