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A166233
Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505526393, 734448519232070580, 30846837807745372371, 1295567187925238776044, 54413821892857220325252
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170762, 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 (41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
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)/(861*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 07 2016 *)
coxG[{10, 861, -41}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 10 2018 *)
PROG
(Sage)
def A166233_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11) ).list()
A166233_list(30) # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A164687 A165175 A165694 * A166437 A166717 A167096
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved