A163968 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 19, 342, 6156, 110808, 1994544, 35901621, 646226100, 11632014567, 209375268012, 3768736928724, 67836942598176, 1221059168656830, 21978960670333953, 395619413496128064, 7121115628832971863, 128179472668131616290, 2307219552362877498072, 41529754741525340825124

Offset

0,2

Comments

The initial terms coincide with those of A170738, 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..795

Index entries for linear recurrences with constant coefficients, signature (17,17,17,17,17,-153).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

a(n) = -153*a(n-6) + 17*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 23 2017 *)
coxG[{6, 153, -17}] (* 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)/(1-18*t+170*t^6-153*t^7)) \\ G. C. Greubel, Aug 23 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7) )); // G. C. Greubel, Aug 11 2019
(Sage)
def A163968_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7)).list()
A163968_list(30) # G. C. Greubel, Aug 11 2019
(GAP) a:=[19, 342, 6156, 110808, 1994544, 35901621];; for n in [7..30] do a[n]:=17*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -153*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019

Crossrefs

Sequence in context: A049664 A163110 A163453 * A164631 A164909 A165341

Adjacent sequences: A163965 A163966 A163967 * A163969 A163970 A163971

Keyword

nonn,easy

Author

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

Status

approved