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A165880 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776793, 36287890202880, 616894133404896, 10487200267134144, 178282404528545952, 3030800876768794752, 51523614901389241440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170737, 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..500

Index entries for linear recurrences with constant coefficients, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, -136).

FORMULA

G.f.: (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)/(136*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).

MATHEMATICA

CoefficientList[Series[(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)/(136*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1), {t, 0, 25}], t] (* G. C. Greubel, Apr 17 2016 *)

coxG[{10, 136, -16}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 04 2017 *)

CROSSREFS

Cf. A154638, A170737.

Sequence in context: A164630 A164892 A165329 * A166412 A166599 A167048

Adjacent sequences:  A165877 A165878 A165879 * A165881 A165882 A165883

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified June 20 17:40 EDT 2019. Contains 324234 sequences. (Running on oeis4.)