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A166425
Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
1
1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305189999999535, 549155699999972100, 16474670999998744965, 494240129999949807900, 14827203899998118005500
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170750, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (29,29,29,29,29,29,29,29,29,29,-435).
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)/(435*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
From G. C. Greubel, Jul 25 2024: (Start)
a(n) = 29*Sum_{j=1..10} a(n-j) - 435*a(n-11).
G.f.: (1+x)*(1-x^11)/(1 - 30*x + 464*x^11 - 435*x^12). (End)
MATHEMATICA
With[{p=435, q=29}, 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 13 2016; Jul 25 2024 *)
coxG[{11, 435, -29}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 26 2021 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-30*x+464*x^11-435*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
def A166425_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^11)/(1-30*x+464*x^11-435*x^12) ).list()
A166425_list(30) # G. C. Greubel, Jul 25 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved