A163969 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 20, 380, 7220, 137180, 2606420, 49521790, 940910400, 17877229200, 339666055200, 6453630356400, 122618507616000, 2329742730783510, 44264942521047180, 841030689999256020, 15979521970107624780

Offset

0,2

Comments

The initial terms coincide with those of A170739, although the two sequences are eventually different.

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

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, 18, -171).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

Mathematica

coxG[{6, 171, -18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 21 2015 *)
CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 23 2017 *)

Prog

(PARI) t='t+O('t^50); Vec((t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)) \\ G. C. Greubel, Aug 23 2017

Crossrefs

Sequence in context: A342886 A163124 A163454 * A164633 A164911 A165348

Adjacent sequences: A163966 A163967 A163968 * A163970 A163971 A163972

Keyword

nonn,easy

Author

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

Status

approved