A163957 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 12, 132, 1452, 15972, 175692, 1932546, 21257280, 233822160, 2571956640, 28290564720, 311185670400, 3422926421970, 37650915208500, 414146038003500, 4555452101075700, 50108275682741100, 551172361422635700

Offset

0,2

Comments

The initial terms coincide with those of A003954, 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..955

Index entries for linear recurrences with constant coefficients, signature (10,10,10,10,10,-55).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).

a(n) = -55*a(n-6) + 10*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)
coxG[{6, 55, -10}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7)) \\ G. C. Greubel, Aug 13 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7) )); // G. C. Greubel, Aug 10 2019
(Sage)
def A163957_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7)).list()
A163957_list(30) # G. C. Greubel, Aug 10 2019
(GAP) a:=[12, 132, 1452, 15972, 175692, 1932546];; for n in [7..30] do a[n]:=10*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -55*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019

Crossrefs

Sequence in context: A010577 A163055 A163432 * A063813 A164601 A164781

Adjacent sequences: A163954 A163955 A163956 * A163958 A163959 A163960

Keyword

nonn

Author

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

Status

approved