A166435 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747904000000000, 429916159999999180, 17196646399999934400, 687865855999996064820, 27514634239999790145600

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..500

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

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)/(780*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).

From G. C. Greubel, Jul 26 2024: (Start)

a(n) = 39*Sum_{j=1..10} a(n-j) - 780*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 40*x + 819*x^11 - 780*x^12). (End)

Mathematica

With[{p=780, q=39}, 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 26 2024 *)
coxG[{11, 780, -39, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 26 2024 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-40*x+819*x^11-780*x^12) )); // G. C. Greubel, Jul 26 2024
(SageMath)
def A166435_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-40*x+819*x^11-780*x^12) ).list()
A166435_list(30) # G. C. Greubel, Jul 26 2024
(PARI) Vec((1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)*(1+x)/(1-39*x-39*x^2-39*x^3-39*x^4-39*x^5-39*x^6-39*x^7-39*x^8-39*x^9-39*x^10+780*x^11)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A154638, A169452, A170760.

Sequence in context: A165173 A165692 A166225 * A166714 A167094 A167598

Adjacent sequences: A166432 A166433 A166434 * A166436 A166437 A166438

Keyword

nonn,easy,changed

Author

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

Status

approved