A167926 - OEIS

A167926

Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104512, 18691697672192, 299067162755072, 4785074604081152, 76561193665298432, 1224979098644774912, 19599665578316398456

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170736, 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 (15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,-120).

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)/( 120*t^16 - 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).

From G. C. Greubel, Sep 10 2023: (Start)

G.f.: (1+t)*(1-t^16)/(1 - 16*t + 135*t^16 - 120*t^17).

a(n) = 15*Sum_{j=1..15} a(n-j) - 120*a(n-16). (End)

MATHEMATICA

coxG[{16, 120, -15}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 27 2015 *)

CoefficientList[Series[(1+t)*(1-t^16)/(1-16*t+135*t^16-120*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 10 2023 *)

PROG

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-16*x+135*x^16-120*x^17) )); // G. C. Greubel, Sep 10 2023

(SageMath)

def A167926_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( (1+x)*(1-x^16)/(1-16*x+135*x^16-120*x^17) ).list()

A167926_list(40) # G. C. Greubel, Sep 10 2023

(PARI) Vec((1+x^2)*(1+x^4)*(1+x^8)*(1+x)^2/(1-15*x-15*x^2-15*x^3-15*x^4-15*x^5-15*x^6-15*x^7-15*x^8-15*x^9-15*x^10-15*x^11-15*x^12-15*x^13-15*x^14-15*x^15+120*x^16)+O(x^99)) \\ Charles R Greathouse IV, May 16 2026

CROSSREFS

Cf. A154638, A169452, A170736.

Cf. A167881, A167882, A167896-A167900, A167908, A167914, A167916, A167919, A167922, A167923, A167924, A167927, A167929, A167931, A167933, A167935, A167937, A167938, A167940-A167947, A167949-A167962, A167978, A167980, A167988, A167989.

Sequence in context: A167027 A167124 A167673 * A168694 A168742 A168790

Adjacent sequences: A167923 A167924 A167925 * A167927 A167928 A167929

KEYWORD

nonn,easy,changed

AUTHOR

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

STATUS

approved