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A165979 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 2
1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332001, 3811511582622900, 99099301147958475, 2576581829840760300, 66991127575699606500, 1741769316964025575200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170746, 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 (25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

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)/(325*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

G.f.: (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11). - G. C. Greubel, Apr 26 2019

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11), {x, 0, 20}], x] (* G. C. Greubel, Apr 20 2016, modified Apr 26 2019 *)

coxG[{10, 325, -25}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

PROG

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)) \\ G. C. Greubel, Apr 26 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11) )); // G. C. Greubel, Apr 26 2019

(Sage) ((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

CROSSREFS

Sequence in context: A164644 A164969 A165445 * A166421 A166614 A167080

Adjacent sequences:  A165976 A165977 A165978 * A165980 A165981 A165982

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 23 12:02 EDT 2019. Contains 326222 sequences. (Running on oeis4.)