A163391 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 9, 72, 576, 4608, 36828, 294336, 2352420, 18801216, 150264576, 1200956652, 9598382640, 76712967828, 613111567824, 4900159716480, 39163451657148, 313005296651040, 2501626174048260, 19993698450611424, 159795249138713664

Offset

0,2

Comments

The initial terms coincide with those of A003951, 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 (7, 7, 7, 7, -28).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(28*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).

a(n) = 7*a(n-1)+7*a(n-2)+7*a(n-3)+7*a(n-4)-28*a(n-5). - Wesley Ivan Hurt, May 10 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-8*x+35*x^5-28*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{7, 7, 7, 7, -28}, {1, 9, 72, 576, 4608, 36828}, 30] (* G. C. Greubel, Dec 21 2016 *)
coxG[{5, 28, -7}] (* 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)/(1-8*x+35*x^5-28*x^6)) \\ G. C. Greubel, Dec 21 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-8*x+35*x^5-28*x^6) )); // G. C. Greubel, May 12 2019
(SageMath) ((1+x)*(1-x^5)/(1-8*x+35*x^5-28*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

Crossrefs

Sequence in context: A006634 A129328 A162960 * A163953 A164375 A164777

Adjacent sequences: A163388 A163389 A163390 * A163392 A163393 A163394

Keyword

nonn

Author

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

Status

approved