A165512 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951338, 306775222626096, 8589706233212790, 240511774521056976, 6734329686340363296, 188561231210551675392, 5279714473700048997888

Offset

0,2

Comments

The initial terms coincide with those of A170748, 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..689

Index entries for linear recurrences with constant coefficients, signature (27,27,27,27,27,27,27,27,-378).

Formula

G.f.: (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)/(378*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 16 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10), {t, 0, 20}], t] (* G. C. Greubel, Oct 21 2018 *)
coxG[{9, 378, -27}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 16 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10)) \\ G. C. Greubel, Oct 21 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10) )); // G. C. Greubel, Oct 21 2018
(Sage)
def A165512_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10)).list()
A165512_list(20) # G. C. Greubel, Sep 16 2019
(GAP) a:=[29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951338];; for n in [10..20] do a[n]:=27*Sum([1..8], j-> a[n-j]) -378*a[n-9]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019

Crossrefs

Sequence in context: A164026 A164665 A164974 * A166004 A166423 A166616

Adjacent sequences: A165509 A165510 A165511 * A165513 A165514 A165515

Keyword

nonn

Author

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

Status

approved