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A166325
Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 50, 2450, 120050, 5882450, 288240050, 14123762450, 692064360050, 33911153642450, 1661646528480050, 81420679895521225, 3989613314880480000, 195491052429140580000, 9579061569027744360000, 469374016882352414700000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170769, 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 (48,48,48,48,48,48,48,48,48,-1176).
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)/(1176*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 12 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{10, 1176, -48}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 12 2020 *)
PROG
(Sage)
def A166325_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11) ).list()
A166325_list(30) # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A164695 A165182 A165726 * A166463 A166856 A167103
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved