login
A166369
Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
1
1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 109999999945, 1099999998900, 10999999983555, 109999999781100, 1099999997266500, 10999999967220000, 109999999617750000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003953, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
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)/(45*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
From G. C. Greubel, Jul 23 2024: (Start)
a(n) = 9*Sum_{j=1..10} a(n-j) - 45*a(n-11).
G.f.: (1+t)*(1-t^11)/(1 - 10*t + 54*t^11 - 45*t^12). (End)
MATHEMATICA
With[{p=45, q=9}, 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 10 2016; Jul 23 2024 *)
coxG[{11, 45, -9}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 12 2016 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-10*x+54*x^11-45*x^12) )); // G. C. Greubel, Jul 23 2024
(SageMath)
def A166369_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^11)/(1-10*x+54*x^11-45*x^12) ).list()
A166369_list(30) # G. C. Greubel, Jul 23 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved