A164071 - OEIS

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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.

1, 38, 1406, 52022, 1924814, 71218118, 2635069663, 97497551520, 3607408444536, 133474076864784, 4938539527424232, 182725913801503872, 6760857008268006426, 250151642617591466280, 9255608309383525500408

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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.

LINKS

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (36, 36, 36, 36, 36, -666).

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

Adjacent sequences: A164068 A164069 A164070 * A164072 A164073 A164074

KEYWORD

nonn

AUTHOR

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

STATUS

approved