A165649 - OEIS

A165649

Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910946, 1449027061218, 47817893019633, 1577990469629376, 52073685497159040, 1718431621386106176, 56708243505076813056, 1871372035645600036032, 61755277175580952960128

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170753, 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 (32, 32, 32, 32, 32, 32, 32, 32, -528).

FORMULA

G.f. (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)/(528*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 -

32*t^2 - 32*t + 1)

MATHEMATICA

coxG[{9, 528, -32}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 24 2022 *)

CROSSREFS

Sequence in context: A164050 A164670 A165166 * A166130 A166428 A166682

Adjacent sequences: A165646 A165647 A165648 * A165650 A165651 A165652

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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