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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A163876 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 27
1, 3, 6, 12, 24, 48, 93, 180, 351, 684, 1332, 2592, 5046, 9825, 19128, 37239, 72498, 141144, 274788, 534972, 1041513, 2027676, 3947595, 7685400, 14962368, 29129580, 56711106, 110408373, 214949232, 418475259, 814711182, 1586125572, 3087958512 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also, coordination sequence for (6,6,6) tiling of hyperbolic plane. - N. J. A. Sloane, Dec 29 2015

The initial terms coincide with those of A003945, 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..1000

J. W. Cannon, P. Wagreich, Growth functions of surface groups, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1.

Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 1, -1).

FORMULA

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

G.f.: (1+x)*(1-x^6)/(1-2*x+2*x^6-x^7). - G. C. Greubel, Apr 25 2019

a(n) = -a(n-6) + Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 07 2021

MATHEMATICA

coxG[{6, 1, -1, 40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 22 2015 *)

CoefficientList[Series[(1+x)*(1-x^6)/(1-2*x+2*x^6-x^7), {x, 0, 40}], x] (* G. C. Greubel, Aug 06 2017, modified Apr 25 2019 *)

PROG

(PARI) x='x+O('x^40); Vec((x^6+2*x^5+2*x^4+2*x^3+2*x^2+2*x+1)/(x^6-x^5- x^4-x^3-x^2-x+1)) \\ G. C. Greubel, Aug 06 2017

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^6)/(1-2*x+2*x^6-x^7) )); // G. C. Greubel, Apr 25 2019

(Sage) ((1+x)*(1-x^6)/(1-2*x+2*x^6-x^7)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

CROSSREFS

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Sequence in context: A001668 A080616 A090572 * A033893 A006851 A164352

Adjacent sequences:  A163873 A163874 A163875 * A163877 A163878 A163879

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 30 16:05 EDT 2022. Contains 354943 sequences. (Running on oeis4.)