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

Author

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

Keywords

• nonn
• easy

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).

Programs

Magma

R:=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

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 *)

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

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

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