A163748 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 44, 1892, 81356, 3498308, 150426298, 6468290136, 278134727640, 11959718115576, 514264646533176, 22113240807047082, 950863378003793100, 40886868257711476308, 1758124284303633320844, 75598869044590717310100

Offset

0,2

Comments

The initial terms coincide with those of A170763, 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..610

Index entries for linear recurrences with constant coefficients, signature (42,42,42,42,-903).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).

a(n) = 42*a(n-1)+42*a(n-2)+42*a(n-3)+42*a(n-4)-903*a(n-5). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 02 2017 *)
coxG[{5, 903, -42}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 09 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6)) \\ G. C. Greubel, Aug 02 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A163748_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6)).list()
A163748_list(20) # G. C. Greubel, Aug 09 2019
(GAP) a:=[44, 1892, 81356, 3498308, 150426298];; for n in [6..30] do a[n]:=42*(a[n-1]+a[n-2]+a[n-3] +a[n-4]) -903*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019

Crossrefs

Sequence in context: A004295 A162882 A163230 * A164277 A164688 A165176

Adjacent sequences: A163745 A163746 A163747 * A163749 A163750 A163751

Keyword

nonn

Author

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

Status

approved