A163959 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 14, 182, 2366, 30758, 399854, 5198011, 67572960, 878433192, 11419432752, 148450042104, 1929816959616, 25087183842630, 326127713832648, 4239586491528024, 55113665158705608, 716465177275138200

Offset

0,2

Comments

The initial terms coincide with those of A170733, 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..895

Index entries for linear recurrences with constant coefficients, signature (12,12,12,12,12,-78).

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(78*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).

a(n) = -78*a(n-6) + 12*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

Maple

seq(coeff(series((1+t)*(1-t^6)/(1-13*t+90*t^6-78*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^6)/(1-13*t+90*t^6-78*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)
coxG[{6, 78, -12}] (* 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)/(1-13*t+90*t^6-78*t^7)) \\ G. C. Greubel, Aug 13 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-13*t+90*t^6-78*t^7) )); // G. C. Greubel, Aug 11 2019
(Sage)
def A163959_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-13*t+90*t^6-78*t^7)).list()
A163959_list(30) # G. C. Greubel, Aug 11 2019
(GAP) a:=[14, 182, 2366, 30758, 399854, 5198011];; for n in [7..30] do a[n]:=12*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -78*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019

Crossrefs

Sequence in context: A342883 A163090 A163439 * A164618 A164835 A165270

Adjacent sequences: A163956 A163957 A163958 * A163960 A163961 A163962

Keyword

nonn

Author

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

Status

approved