A167943 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852

Offset

0,2

Comments

The initial terms coincide with those of A170747, 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..500

Index entries for linear recurrences with constant coefficients, signature (26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,-351).

Formula

G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/( 351*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

a(n) = -351*a(n-16) + 26*Sum_{k=1..15} a(n-k). - Wesley Ivan Hurt, Sep 03 2022

G.f.: (1+t)*(1-t^16)/(1 - 27*t + 377*t^16 - 351*t^17). - G. C. Greubel, Sep 08 2023

Mathematica

CoefficientList[Series[(1+t)*(1-t^16)/(1-27*t+377*t^16-351*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016; Sep 08 2023 *)
coxG[{16, 35, -26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 20 2021 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-27*x+377*x^16-351*x^17) )); // G. C. Greubel, Sep 08 2023
(SageMath)
def A167943_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-27*x+377*x^16-351*x^17) ).list()
A167943_list(40) # G. C. Greubel, Sep 08 2023

Crossrefs

Cf. A154638, A169452, A170747.

Sequence in context: A167235 A063817 A167699 * A168705 A168753 A168801

Adjacent sequences: A167940 A167941 A167942 * A167944 A167945 A167946

Keyword

nonn

Author

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

Status

approved