A166433 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949251072, 244850262071539995, 9304309958718491652, 353563778431301613513, 13435423580389420681500

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..500

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

Formula

G.f.: (t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).

From G. C. Greubel, Jul 25 2024: (Start)

a(n) = 37*Sum_{j=1..10} a(n-j) - 703*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 38*x + 740*x^11 - 703*x^12). (End)

Mathematica

With[{p=703, q=37}, CoefficientList[Series[(1+t)*(1-t^11)/(1 - (q+1)*t + (p+q)*t^11 - p*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 14 2016; Jul 25 2024 *)
coxG[{11, 703, -37}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 06 2019 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-38*x+740*x^11-703*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
def A166423_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-38*x+740*x^11-703*x^12) ).list()
A166423_list(30) # G. C. Greubel, Jul 25 2024

Crossrefs

Cf. A154638, A169452, A170758.

Sequence in context: A165171 A165688 A166171 * A166691 A167092 A167537

Adjacent sequences: A166430 A166431 A166432 * A166434 A166435 A166436

Keyword

nonn

Author

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

Status

approved