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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, -561).

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

Adjacent sequences: A164065 A164066 A164067 * A164069 A164070 A164071

KEYWORD

nonn

AUTHOR

John Cannon and N. J. A. Sloane, Dec 03 2009

STATUS

approved

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Last modified January 31 15:11 EST 2023. Contains 359976 sequences. (Running on oeis4.)