A163525 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 25, 600, 14400, 345600, 8294100, 199051200, 4777056300, 114645211200, 2751385708800, 66030872460900, 1584683711924400, 38031035684483100, 912711895976984400, 21904294481198985600, 525684083700365474100

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170744, 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..720
• Index entries for linear recurrences with constant coefficients, signature (23, 23, 23, 23, -276).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6) )); // G. C. Greubel, May 16 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 276, -23}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6)) \\ G. C. Greubel, Jul 27 2017

Sage

((1+x)*(1-x^5)/(1-24*x+299*x^5-276*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)/(276*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

a(n) = 23*a(n-1)+23*a(n-2)+23*a(n-3)+23*a(n-4)-276*a(n-5). - Wesley Ivan Hurt, May 10 2021