A163526 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 26, 650, 16250, 406250, 10155925, 253890000, 6347047200, 158671110000, 3966651000000, 99163106355300, 2478998445300000, 61972980856207200, 1549275016079700000, 38730637808401500000, 968235006358878382800

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170745, 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..710
• Index entries for linear recurrences with constant coefficients, signature (24, 24, 24, 24, -300).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6) )); // G. C. Greubel, May 16 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 300, -24}] (* 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)/(1-25*x+324*x^5-300*x^6)) \\ G. C. Greubel, Jul 27 2017

Sage

((1+x)*(1-x^5)/(1-25*x+324*x^5-300*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)/(300*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).

a(n) = 24*a(n-1)+24*a(n-2)+24*a(n-3)+24*a(n-4)-300*a(n-5). - Wesley Ivan Hurt, May 10 2021