A162851 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 37, 1332, 47286, 1678320, 59557050, 2113447770, 74997827100, 2661373678950, 94441530616650, 3351353019273000, 118926143828399250, 4220214225380039250, 149758560520153357500, 5314333645481777358750, 188584492248078150341250

Offset

0,2

Comments

The initial terms coincide with those of A170756, 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..643

Index entries for linear recurrences with constant coefficients, signature (35, 35, -630).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(630*t^3 - 35*t^2 - 35*t + 1).

G.f.: (1+x)*(1-x^3)/(1 - 36*x + 665*x^3 - 630*x^4). - G. C. Greubel, Apr 26 2019

a(n) = 35*a(n-1)+35*a(n-2)-630*a(n-3). - Wesley Ivan Hurt, May 05 2021

Mathematica

CoefficientList[Series[(t^3+2*t^2+2*t+1)/(630*t^3-35*t^2-35*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{35, 35, -630}, {1, 37, 1332}, 20] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 630, -35}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(630*t^3-35*t^2-35*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 +2*t^2+2*t+1)/(630*t^3-35*t^2-35*t+1))); // G. C. Greubel, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1-36*x+665*x^3-630*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
(GAP) a:=[37, 1332, 47286];; for n in [4..20] do a[n]:=35*a[n-1]+ 35*a[n-2]-630*a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Apr 26 2019

Crossrefs

Sequence in context: A246461 A006062 A219420 * A163220 A163645 A164070

Adjacent sequences: A162848 A162849 A162850 * A162852 A162853 A162854

Keyword

nonn

Author

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

Status

approved