A163600 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 35, 1190, 40460, 1375640, 46771165, 1590199380, 54066091695, 1838223751980, 62498813135220, 2124932636259510, 72246791293015185, 2456359680805901640, 83515167573569420535, 2839479604449882838290, 96541079403144247211340

Offset

0,2

Comments

The initial terms coincide with those of A170754, 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..650

Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, -561).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

a(n) = 33*a(n-1)+33*a(n-2)+33*a(n-3)+33*a(n-4)-561*a(n-5). - Wesley Ivan Hurt, May 11 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 29 2017 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6)) \\ G. C. Greubel, Jul 29 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A029546 A305539 A163218 * A164068 A164671 A165167

Adjacent sequences: A163597 A163598 A163599 * A163601 A163602 A163603

Keyword

nonn

Author

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

Status

approved