A163514 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 22, 462, 9702, 203742, 4278351, 89840520, 1886549280, 39615400440, 831878586000, 17468509071090, 366818925627000, 7702782398341800, 161749714998425400, 3396561002126245800, 71323937982067871100

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170741, 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..750
• Index entries for linear recurrences with constant coefficients, signature (20, 20, 20, 20, -210).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6) )); // G. C. Greubel, May 16 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 210, -20}] (* 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)/(1-21*x+230*x^5-210*x^6)) \\ G. C. Greubel, Jul 27 2017

Sage

((1+x)*(1-x^5)/(1-21*x+230*x^5-210*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)/(210*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

a(n) = -210*a(n-5) + 20*Sum_{k=1..4} a(n-k). - Wesley Ivan Hurt, May 05 2021