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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A163224 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 1
1, 41, 1640, 65600, 2623180, 104894400, 4194464820, 167726145600, 6706948607580, 268194081870000, 10724409825744420, 428842296999090000, 17148329715447559980, 685718769084764781600, 27420176663127165184020 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170760, 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..620

Index entries for linear recurrences with constant coefficients, signature (39,39,39,-780).

FORMULA

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).

a(n) = 39*a(n-1)+39*a(n-2)+39*a(n-3)-780*a(n-4). - Wesley Ivan Hurt, May 06 2021

MATHEMATICA

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3-39*t^2 - 39*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {39, 39, 39, -780}, {41, 1640, 65600, 2623180} 20]] (* G. C. Greubel, Dec 11 2016 *)

coxG[{4, 780, -39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 18 2019 *)

PROG

(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3- 39*t^2-39*t+1)) \\ G. C. Greubel, Dec 11 2016

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-40*x+819*x^4-780*x^5) )); // G. C. Greubel, Apr 30 2019

(Sage) ((1+x)*(1-x^4)/(1-40*x+819*x^4-780*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

CROSSREFS

Sequence in context: A180667 A281608 A162878 * A163677 A164091 A164685

Adjacent sequences:  A163221 A163222 A163223 * A163225 A163226 A163227

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 December 9 05:44 EST 2021. Contains 349627 sequences. (Running on oeis4.)