A166075 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610172999999535, 18305189999972100, 549155699998744965, 16474670999949807900, 494240129998118005500, 14827203899932253220000

Offset

0,2

Comments

The initial terms coincide with those of A170750, 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..500

Index entries for linear recurrences with constant coefficients, signature (29,29,29,29,29,29,29,29,29,-435).

Formula

G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Dec 05 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 24 2016 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11)) \\ G. C. Greubel, Dec 05 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11) )); // G. C. Greubel, Dec 05 2019
(Sage)
def A166075_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11)).list()
A166075_list(30) # G. C. Greubel, Dec 05 2019
(GAP) a:=[31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610172999999535];; for n in [11..30] do a[n]:=29*Sum([1..9], j-> a[n-j]) - 435*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Dec 05 2019

Crossrefs

Sequence in context: A164667 A164992 A165547 * A166425 A166618 A167084

Adjacent sequences: A166072 A166073 A166074 * A166076 A166077 A166078

Keyword

nonn

Author

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

Status

approved