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

Author

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

Keywords

• nonn

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).

Programs

Magma

R:=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

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 *)

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

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

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