A162983 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 10, 90, 810, 7245, 64800, 579600, 5184000, 46366380, 414707040, 3709193760, 33175513440, 296726124240, 2653957198080, 23737339710720, 212309865780480, 1898927161041600, 16984252473131520, 151909371770042880

Offset

0,2

Comments

The initial terms coincide with those of A003952, 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..1000

Index entries for linear recurrences with constant coefficients, signature (8, 8, 8, -36).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

From G. C. Greubel, Apr 28 2019: (Start)

a(n) = 8*(a(n-1) + a(n-2) + a(n-3)) - 36*a(n-4).

G.f.: (1+x)*(1-x^4)/(1 - 9*x + 44*x^4 - 36*x^5). (End)

Mathematica

CoefficientList[Series[(1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5), {x, 0, 20}], x]
(* or *) coxG[{4, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5)) \\ G. C. Greubel, Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[10, 90, 810, 7245];; for n in [5..20] do a[n]:=8*(a[n-1]+a[n-2] +a[n-3]) - 36*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A092420 A010579 A010576 * A163397 A163954 A164548

Adjacent sequences: A162980 A162981 A162982 * A162984 A162985 A162986

Keyword

nonn

Author

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

Status

approved