A167940 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset

0,2

Comments

The initial terms coincide with those of A170744, 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 (23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,-276).

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)/( 276*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

From G. C. Greubel, Sep 08 2023: (Start)

G.f.: (1+t)*(1-t^16)/(1 - 24*t + 299*t^16 - 276*t^17).

a(n) = 23*Sum_{j=1..15} a(n-j) - 276*a(n-16). (End)

Mathematica

coxG[{16, 276, -23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 05 2015 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-24*t+299*t^16-276*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 08 2023 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-24*x+299*x^16-276*x^17) )); // G. C. Greubel, Sep 08 2023
(SageMath)
def A167940_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-24*x+299*x^16-276*x^17) ).list()
A167940_list(40) # G. C. Greubel, Sep 08 2023

Crossrefs

Cf. A154638, A169452, A170758.

Sequence in context: A167078 A167212 A167696 * A168702 A168750 A168798

Adjacent sequences: A167937 A167938 A167939 * A167941 A167942 A167943

Keyword

nonn

Author

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

Status

approved