A163567 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 33, 1056, 33792, 1081344, 34602480, 1107262464, 35431858704, 1133802193920, 36281117097984, 1160978047975152, 37150731170716416, 1188805274075570448, 38041188830863975680, 1217299484804824768512, 38952989673757190287344

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170752, 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..660
• Index entries for linear recurrences with constant coefficients, signature (31, 31, 31, 31, -496).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-32*x+527*x^5-496*x^6) )); // G. C. Greubel, May 18 2019

Mathematica

coxG[{5,496,-31}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 08 2015 *)
CoefficientList[Series[(1+x)*(1-x^5)/(1-32*x+527*x^5-496*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 28 2017 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-32*x+527*x^5-496*x^6)) \\ G. C. Greubel, Jul 28 2017

Sage

((1+x)*(1-x^5)/(1-32*x+527*x^5-496*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 18 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(496*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).

a(n) = 31*a(n-1)+31*a(n-2)+31*a(n-3)+31*a(n-4)-496*a(n-5). - Wesley Ivan Hurt, May 11 2021