A164069 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 36, 1260, 44100, 1543500, 54022500, 1890786870, 66177518400, 2316212372880, 81067406061600, 2837358267534000, 99307506301920000, 3475761563405646270, 121651614218556733500, 4257805080127526578980, 149023128191211379381500

Offset

0,2

Comments

The initial terms coincide with those of A170755, 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..645

Index entries for linear recurrences with constant coefficients, signature (34,34,34,34,34,-595).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(595*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

a(n) = -595*a(n-6) + 34*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 09 2017 *)
coxG[{6, 595, -34}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 13 2019 *)

Prog

(PARI) t='t+O('t^50); Vec((1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7)) \\ G. C. Greubel, Sep 09 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7) )); // G. C. Greubel, Aug 13 2019
(Sage)
def A164069_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7)).list()
A164069_list(30) # G. C. Greubel, Aug 13 2019
(GAP) a:=[36, 1260, 44100, 1543500, 54022500, 1890786870];; for n in [7..30] do a[n]:=34*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -595*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019

Crossrefs

Sequence in context: A162850 A163219 A163601 * A164672 A165168 A165651

Adjacent sequences: A164066 A164067 A164068 * A164070 A164071 A164072

Keyword

nonn

Author

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

Status

approved