login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A164026 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 29, 812, 22736, 636608, 17825024, 499100266, 13974796080, 391293972342, 10956222324432, 306773975852064, 8589664345360896, 240510406272356430, 6734285904493468188, 188559852134231228994, 5279671570397554562148 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170748, 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..685

Index entries for linear recurrences with constant coefficients, signature (27,27,27,27,27,-378).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).

a(n) = -378*a(n-6) + 27*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 07 2017 *)

coxG[{6, 378, -27}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 14 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7)) \\ G. C. Greubel, Sep 07 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7) )); // G. C. Greubel, Aug 13 2019

(Sage)

def A164026_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7)).list()

A164026_list(30) # G. C. Greubel, Aug 13 2019

(GAP) a:=[29, 812, 22736, 636608, 17825024, 499100266];; for n in [7..30] do a[n]:=27*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -378*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019

CROSSREFS

Sequence in context: A162831 A163207 A163549 * A164665 A164974 A165512

Adjacent sequences:  A164023 A164024 A164025 * A164027 A164028 A164029

KEYWORD

nonn

AUTHOR

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 30 23:02 EDT 2021. Contains 346365 sequences. (Running on oeis4.)