login
A164779
Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.
3
1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829645, 430466400, 3874194000, 34867713600, 313809130800, 2824279552800, 25418492355600, 228766218624000, 2058894054430380, 18530029271219040, 166770108473225760
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003952, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/( 36*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
G.f.: (1+x)*(1-x^8)/(1 -9*x +44*x^8 -36*x^9). - G. C. Greubel, Apr 26 2019
MATHEMATICA
coxG[{8, 36, -8}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 13 2017 *)
CoefficientList[Series[(1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9), {x, 0, 20}], x] (* G. C. Greubel, Apr 26 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
CROSSREFS
Sequence in context: A163397 A163954 A164548 * A165219 A165788 A166368
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved