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A164071
Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
0
1, 38, 1406, 52022, 1924814, 71218118, 2635069663, 97497551520, 3607408444536, 133474076864784, 4938539527424232, 182725913801503872, 6760857008268006426, 250151642617591466280, 9255608309383525500408
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170757, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).
MATHEMATICA
CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Sep 09 2017 *)
coxG[{6, 666, -36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 08 2023 *)
PROG
(PARI) t='t+O('t^50); Vec((t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1)) \\ G. C. Greubel, Sep 09 2017
CROSSREFS
Sequence in context: A162858 A163221 A163660 * A164674 A165170 A165687
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved