A163803 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 47, 2162, 99452, 4574792, 210439351, 9680160420, 445285093005, 20483009107740, 942213581113500, 43341602191631640, 1993703464046530125, 91709888457205975050, 4218633208251709753275, 194056131188825472581550

Offset

0,2

Comments

The initial terms coincide with those of A170766, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Colin Barker, Table of n, a(n) for n = 0..600

Index entries for linear recurrences with constant coefficients, signature (45,45,45,45,-1035).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).

a(n) = 45*a(n-1)+45*a(n-2)+45*a(n-3)+45*a(n-4)-1035*a(n-5). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 04 2017 *)
coxG[{5, 1035, -45}] (* 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)/(1-46*t+1080*t^5-1035*t^6)) \\ G. C. Greubel, Aug 04 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A163803_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6)).list()
A163803_list(20) # G. C. Greubel, Aug 09 2019
(GAP) a:=[47, 2162, 99452, 4574792, 210439351];; for n in [6..30] do a[n]:=45*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1035*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019

Crossrefs

Sequence in context: A189173 A162896 A163265 * A164332 A164692 A165179

Adjacent sequences: A163800 A163801 A163802 * A163804 A163805 A163806

Keyword

nonn,easy

Author

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

Status

approved