A163877 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A163877

Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 4, 12, 36, 108, 324, 966, 2880, 8592, 25632, 76464, 228096, 680430, 2029788, 6055044, 18062748, 53882820, 160737372, 479494254, 1430375112, 4266939480, 12728669832, 37970783640, 113270312520, 337895678406, 1007973642420

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003946, 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..25.

Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, 2, -3).

FORMULA

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

MATHEMATICA

CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^6 - 2*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 07 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)/(3*t^6 - 2*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1)) \\ G. C. Greubel, Aug 07 2017

CROSSREFS

Sequence in context: A003119 A001394 A156946 * A336262 A164353 A347506

Adjacent sequences: A163874 A163875 A163876 * A163878 A163879 A163880

KEYWORD

nonn

AUTHOR

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

STATUS

approved