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A167929 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I. 2
1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305856, 1221099791505408, 21979796247097344, 395636332447752192, 7121453984059539456 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170738, 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 (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).

FORMULA

G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*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)/( 153*t^16 - 17*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

G.f.: (1+x)*(1-x^16)/(1 - 18*x + 170*x^16 - 153*x^17). - G. C. Greubel, Apr 26 2019

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^16)/(1-18*x+170*x^16-153*x^17), {x, 0, 20}], x] (* G. C. Greubel, Jul 01 2016, modified Apr 26 2019 *)

coxG[{16, 153, -17}] (* 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^16)/(1-18*x+170*x^16-153*x^17)) \\ G. C. Greubel, Apr 26 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^16)/(1-18*x+170*x^16-153*x^17) )); // G. C. Greubel, Apr 26 2019

(Sage) ((1+x)*(1-x^16)/(1-18*x+170*x^16-153*x^17)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

CROSSREFS

Cf. A154638, A170738.

Sequence in context: A167049 A167126 A167676 * A168696 A168744 A168792

Adjacent sequences:  A167926 A167927 A167928 * A167930 A167931 A167932

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified April 11 03:59 EDT 2021. Contains 342886 sequences. (Running on oeis4.)