A163668 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 39, 1482, 56316, 2140008, 81319563, 3090115236, 117423309705, 4462045136796, 169556171182476, 6443075832883092, 244834652131935645, 9303632060115383718, 353534798919570074859, 13434200024194718979990

Offset

0,2

Comments

The initial terms coincide with those of A170758, 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..630

Index entries for linear recurrences with constant coefficients, signature (37, 37, 37, 37, -703).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).

a(n) = 37*a(n-1)+37*a(n-2)+37*a(n-3)+37*a(n-4)-703*a(n-5). - Wesley Ivan Hurt, May 11 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 01 2017 *)
coxG[{5, 703, -37}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 23 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6)) \\ G. C. Greubel, Aug 01 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6) )); // G. C. Greubel, May 23 2019
(Sage) ((1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 23 2019
(GAP) a:=[39, 1482, 56316, 2140008, 81319563];; for n in [6..20] do a[n]:=37*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) -703*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, May 23 2019

Crossrefs

Sequence in context: A097314 A162871 A163222 * A164084 A164681 A165171

Adjacent sequences: A163665 A163666 A163667 * A163669 A163670 A163671

Keyword

nonn

Author

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

Status

approved