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A166128
Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909140976, 26228105183354880, 813071260683525120, 25205209081174517760, 781361481515952460800, 24222205926980341002240
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170751, 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 (30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
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)/(465*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*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 -31*t +495*t^10 -465*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 26 2016 *)
coxG[{465, 10, -30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 11 2020 *)
PROG
(Sage)
def A166128_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*t^11) ).list() A166128_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164668 A165131 A165548 * A166426 A166622 A167085
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved