A163215 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 32, 992, 30752, 952816, 29521920, 914703360, 28341043200, 878114994960, 27207394552800, 842990180666400, 26119092121336800, 809270367424023600, 25074322053313752000, 776899354951763496000, 24071343043338616536000

Offset

0,2

Comments

The initial terms coincide with those of A170751, 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..665

Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, -465).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

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

a(n) = 30*(a(n-1) + a(n-2) + a(n-3)) - 465*a(n-4).

G.f.: (1+x)*(1-x^4)/(1 - 31*x + 495*x^4 - 465*x^5). (End)

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(465*t^4-30*t^3-30*t^2 - 30*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{30, 30, 30, -465}, {1, 32, 992, 30752, 952816}, 20] (* G. C. Greubel, Dec 10 2016 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5)) \\ G. C. Greubel, Dec 10 2016, modified Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-31*x+495*x^4-465*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[32, 992, 30752, 952816];; for n in [5..20] do a[n]:=30*(a[n-1]+a[n-2] +a[n-3]) -465*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A264344 A228983 A162836 * A163565 A164036 A164668

Adjacent sequences: A163212 A163213 A163214 * A163216 A163217 A163218

Keyword

nonn

Author

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

Status

approved