A163347 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 8, 56, 392, 2744, 19180, 134064, 937104, 6550320, 45786384, 320044452, 2237094216, 15637173048, 109303031880, 764022547512, 5340478146444, 37329666414768, 260932440209616, 1823904280240560, 12748996716570576

Offset

0,2

Comments

The initial terms coincide with those of A003950, 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

Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, 6, -21).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(21*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

a(n) = 6*a(n-1)+6*a(n-2)+6*a(n-3)+6*a(n-4)-21*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-7*x+27*x^5-21*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, 6, 6, 6, -21}, {1, 8, 56, 392, 2744, 19180}, 30] (* G. C. Greubel, Dec 19 2016 *)
coxG[{5, 21, -6}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-7*x+27*x^5-21*x^6)) \\ G. C. Greubel, Dec 19 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-7*x+27*x^5-21*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-7*x+27*x^5-21*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

Crossrefs

Sequence in context: A162949 A063812 A234274 * A163924 A164373 A164769

Adjacent sequences: A163344 A163345 A163346 * A163348 A163349 A163350

Keyword

nonn

Author

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

Status

approved