A164548 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314365, 47828880, 430456320, 3874074480, 34866378720, 313794784080, 2824129437120, 25416952359660, 228750658083360, 2058738704511840, 18528493377756960, 166755045745830240

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 (8,8,8,8,8,8,-36).

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

G.f.: (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8). - G. C. Greubel, Jul 17 2021

Mathematica

CoefficientList[Series[(1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8), {t, 0, 30}], t] (* or *)
coxG[{7, 36, -8, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 17 2021 *)

Prog

(Magma)
R<t>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) )); // G. C. Greubel, Jul 17 2021
(SageMath)
def A168823_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) ).list()
A168823_list(30) # G. C. Greubel, Jul 17 2021
(PARI) a(n)=if(n, ([0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1; -36, 8, 8, 8, 8, 8, 8]^(n-1)*[10; 90; 810; 7290; 65610; 590490; 5314365])[1, 1], 1) \\ Charles R Greathouse IV, Jun 05 2026

Crossrefs

Cf. A003952, A154638.

Sequence in context: A162983 A163397 A163954 * A164779 A165219 A165788

Adjacent sequences: A164545 A164546 A164547 * A164549 A164550 A164551

Keyword

nonn,easy,changed

Author

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

Status

approved