A163965 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 17, 272, 4352, 69632, 1114112, 17825656, 285208320, 4563298440, 73012220160, 1168186644480, 18690844262400, 299051235428280, 4784783402808000, 76555952624637000, 1224885932940283200, 19598025983313945600

Offset

0,2

Comments

The initial terms coincide with those of A170736, 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..825

Index entries for linear recurrences with constant coefficients, signature (15,15,15,15,15,-120).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(120*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).

a(n) = -120*a(n-6) + 15*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 23 2017 *)
coxG[{6, 120, -15}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 11 2019 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7)) \\ G. C. Greubel, Aug 23 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7) )); // G. C. Greubel, Aug 11 2019
(Sage)
def A163965_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7)).list()
A163965_list(30) # G. C. Greubel, Aug 11 2019
(GAP) a:=[17, 272, 4352, 69632, 1114112, 17825656];; for n in [7..30] do a[n]:=15*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -120*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019

Crossrefs

Sequence in context: A097830 A163093 A163451 * A164628 A164868 A165321

Adjacent sequences: A163962 A163963 A163964 * A163966 A163967 A163968

Keyword

nonn

Author

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

Status

approved