A166439 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777927680, 1223881242228816930, 53850774658067901360, 2369434084954985744190, 104255099738019288455760

Offset

0,2

Comments

The initial terms coincide with those of A170764, 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 (43,43,43,43,43,43,43,43,43,43,-946).

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)/(946*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).

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

a(n) = 43*Sum_{j=1..10} a(n-j) - 946*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 44*x + 989*x^11 - 946*x^12). (End)

Mathematica

coxG[{11, 946, -43}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 08 2015 *)
With[{p=946, q=43}, 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 *)

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(946, 43, 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 A166439_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( f(946, 43, x) ).list()
A166439_list(30) # G. C. Greubel, Jul 26 2024

Crossrefs

Cf. A154638, A169452, A170764.

Sequence in context: A165177 A165699 A166258 * A166738 A167098 A167642

Adjacent sequences: A166436 A166437 A166438 * A166440 A166441 A166442

Keyword

nonn

Author

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

Status

approved