A166438 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812214444, 22114074925221092, 950905221784506010, 40888924536733717752, 1758223755079548115128, 75603621468420493777560

Offset

0,2

Comments

The initial terms coincide with those of A170763, 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 (42,42,42,42,42,42,42,42,42,42,-903).

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)/(903*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).

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

a(n) = 42*Sum_{j=1..10} a(n-j) - 903*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 43*x + 945*x^11 - 903*x^12). (End)

Mathematica

With[{p=903, q=42}, 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, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 01 2022 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
f:= func< p, q, x | (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12) >;
Coefficients(R!( f(903, 42, x) )); // G. C. Greubel, Jul 26 2024
(SageMath)
def f(p, q, x): return (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12)
def A166438_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( f(903, 42, x) ).list()
A166438_list(30) # G. C. Greubel, Jul 26 2024

Crossrefs

Cf. A154638, A169452, A170763.

Sequence in context: A165176 A165695 A166254 * A166723 A167097 A167641

Adjacent sequences: A166435 A166436 A166437 * A166439 A166440 A166441

Keyword

nonn

Author

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

Status

approved