A163519 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 24, 552, 12696, 292008, 6715908, 154459536, 3552423600, 81702391056, 1879077904176, 43217018799372, 993950655137880, 22859927229943848, 525756756894338904, 12091909332851083560, 278102505382114851108

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170743, 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..730
• Index entries for linear recurrences with constant coefficients, signature (22, 22, 22, 22, -253).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6) )); // G. C. Greubel, May 16 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5,253,-22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 16 2018 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6)) \\ G. C. Greubel, Jul 27 2017

Sage

((1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

a(n) = 22*a(n-1)+22*a(n-2)+22*a(n-3)+22*a(n-4)-253*a(n-5). - Wesley Ivan Hurt, May 10 2021