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A164068
Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
0
1, 35, 1190, 40460, 1375640, 46771760, 1590239245, 54068114100, 1838315192175, 62502693168300, 2125090773290100, 72253059281172000, 2456603097196693830, 83524474080352031265, 2839831057104956921160, 96554219846263616159415
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.
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).
MATHEMATICA
CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Sep 09 2017 *)
coxG[{6, 561, -33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 27 2018 *)
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)/(561*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1)) \\ G. C. Greubel, Sep 09 2017
CROSSREFS
Sequence in context: A305539 A163218 A163600 * A164671 A165167 A165650
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved