A165882 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955390, 122621325148800, 2329805177758800, 44266298376117600, 841059669121542000, 15980133712840142400

Offset

0,2

Comments

The initial terms coincide with those of A170739, 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 (18,18,18,18,18,18,18,18,18,-171).

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)/(171*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 24 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11), {t, 0, 20}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10, 171, -18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 18 2018 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11)) \\ G. C. Greubel, Sep 24 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11) )); // G. C. Greubel, Sep 24 2019
(Sage)
def A165882_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-19*t+189*t^10-171*t^11)).list()
A165882_list(20) # G. C. Greubel, Sep 24 2019
(GAP) a:=[20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955390];; for n in [11..20] do a[n]:=18*Sum([1..9], j-> a[n-j]) -171*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 24 2019

Crossrefs

Cf. A154638, A170739.

Sequence in context: A164633 A164911 A165348 * A063815 A166414 A166601

Adjacent sequences: A165879 A165880 A165881 * A165883 A165884 A165885

Keyword

nonn

Author

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

Status

approved