A163967 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 18, 306, 5202, 88434, 1503378, 25557273, 434471040, 7385963616, 125560632384, 2134518016032, 36286589786112, 616868346117816, 10486699320193920, 178272824864888448, 3030619941978033024, 51520231643134128768

Offset

0,2

Comments

The initial terms coincide with those of A170737, 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..800

Index entries for linear recurrences with constant coefficients, signature (16,16,16,16,16,-136).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).

a(n) = -136*a(n-6) + 16*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-17*t+152*t^6-136*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^6)/(1-17*t+152*t^6-136*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 23 2017 *)
coxG[{6, 136, -16}] (* 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)/(1-17*t+152*t^6-136*t^7)) \\ G. C. Greubel, Aug 23 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-17*t+152*t^6-136*t^7) )); // G. C. Greubel, Aug 11 2019
(Sage)
def A163967_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-17*t+152*t^6-136*t^7)).list()
A163967_list(30) # G. C. Greubel, Aug 11 2019
(GAP) a:=[18, 306, 5202, 88434, 1503378, 25557273];; for n in [7..30] do a[n]:=16*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -136*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019

Crossrefs

Sequence in context: A342885 A163104 A163452 * A164630 A164892 A165329

Adjacent sequences: A163964 A163965 A163966 * A163968 A163969 A163970

Keyword

nonn

Author

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

Status

approved