A162878 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 41, 1640, 64780, 2558400, 101024820, 3989217180, 157523886000, 6220211664420, 245620097065980, 9698903409405600, 382984651654144020, 15123074971766970780, 597171180654087109200, 23580747941118076783620

Offset

0,2

Comments

The initial terms coincide with those of A170760, 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..615

Index entries for linear recurrences with constant coefficients, signature (39, 39, -780).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(780*t^3 - 39*t^2 - 39*t + 1).

a(n) = 39*a(n-1) + 39*a(n-2) - 780*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018

G.f.: (1+x)*(1-x^3)/(1 - 40*x + 819*x^3 - 780*x^4). - G. C. Greubel, Apr 27 2019

Maple

seq(coeff(series((x^3+2*x^2+2*x+1)/(780*x^3-39*x^2-39*x+1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 20182018

Mathematica

CoefficientList[Series[(t^3+2*t^2+2*t+1)/(780*t^3-39*t^2-39*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 780, -39}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 27 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(780*t^3-39*t^2-39*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(780*t^3-39*t^2-39*t+1))); // G. C. Greubel, Oct 24 2018
(GAP) a:=[41, 1640, 64780];; for n in [4..20] do a[n]:=39*a[n-1]+39*a[n-2] -780*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1-40*x+819*x^3-780*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019

Crossrefs

Sequence in context: A305863 A180667 A281608 * A163224 A163677 A164091

Adjacent sequences: A162875 A162876 A162877 * A162879 A162880 A162881

Keyword

nonn

Author

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

Status

approved