A164681 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518235, 4462207664772, 169563890192073, 6443427786666780, 244850254349321868, 9304309606601631648, 353563762821303227856, 13435422902486289765684

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

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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

Formula

G.f.: (x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/(703*x^7 - 37*x^6 - 37*x^5 - 37*x^4 - 37*x^3 - 37*x^2 - 37*x + 1).

G.f.: (1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8). - G. C. Greubel, Apr 26 2019

Mathematica

CoefficientList[Series[(x^7 + 2 x^6 + 2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 + 2 x + 1)/(703 x^7 - 37 x^6 - 37 x^5 - 37 x^4 - 37 x^3 - 37 x^2 - 37 x + 1), {x, 0, 20}], x ] (* Vincenzo Librandi, Apr 29 2014 *)
coxG[{7, 703, -37}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^7)/(1-38*x+740*x^7-703*x^8)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

Crossrefs

Sequence in context: A163222 A163668 A164084 * A165171 A165688 A166171

Adjacent sequences: A164678 A164679 A164680 * A164682 A164683 A164684

Keyword

nonn,easy

Author

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

Status

approved