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

0,2

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).

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

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 *)

Prog

(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
(Magma) R<x>:=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
(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

Crossrefs

Sequence in context: A162837 A324951 A163216 * A164049 A164669 A165140

Adjacent sequences: A163564 A163565 A163566 * A163568 A163569 A163570

Keyword

nonn,easy

Author

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

Status

approved