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A166467 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I. 1
1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6141, 12276, 24543, 49068, 98100, 196128, 392112, 783936, 1567296, 3133440, 6264576, 12524544, 25039878, 50061345, 100085880, 200098167, 400049202, 799804248, 1599020400, 3196865040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003945, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1).

FORMULA

G.f.: (t^12 + 2*t^11 + 2*t^10 + 2*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)/(t^12 - t^11 - t^10 - t^9 - t^8 - t^7 - t^6 - t^5 - t^4 - t^3 - t^2 - t + 1).

MATHEMATICA

CoefficientList[Series[(t^12 + 2*t^11 + 2*t^10 + 2*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)/(t^12 - t^11 - t^10 - t^9 - t^8 - t^7 - t^6 - t^5 - t^4 - t^3 - t^2 - t + 1), {t, 0, 10}], t] (* G. C. Greubel, May 15 2016 *)

coxG[{12, 1, -1, 40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 15 2020 *)

CROSSREFS

Sequence in context: A046944 A165745 A166327 * A166857 A167104 A167648

Adjacent sequences:  A166464 A166465 A166466 * A166468 A166469 A166470

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified March 2 19:18 EST 2021. Contains 341756 sequences. (Running on oeis4.)