A164601 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 12, 132, 1452, 15972, 175692, 1932612, 21258666, 233844600, 2572282680, 28295022360, 311244287640, 3423676622520, 37660326891000, 414262320281370, 4556871492422700, 50125432079728500, 551378055176107500

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..950

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

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).

a(n) = -55*a(n-7) + 10*Sum_{k=1..6} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 28 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8), {t, 0, 30}], t] (* G. C. Greubel, Aug 11 2017 *)
coxG[{7, 55, -10}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 28 2019 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8)) \\ G. C. Greubel, Aug 11 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8) )); // G. C. Greubel, Aug 28 2019
(Sage)
def A164601_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8)).list()
A164601_list(30) # G. C. Greubel, Aug 28 2019
(GAP) a:=[12, 132, 1452, 15972, 175692, 1932612, 21258666];; for n in [8..30] do a[n]:=10*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -55*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Aug 28 2019

Crossrefs

Sequence in context: A163432 A163957 A063813 * A164781 A165266 A165807

Adjacent sequences: A164598 A164599 A164600 * A164602 A164603 A164604

Keyword

nonn

Author

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

Status

approved