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A167937
Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
6
1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460544, 295665060514131968, 6504631331310903296, 143101889288839872512
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170742, 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 (21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,-231).
FORMULA
G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*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)/( 231*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).
From G. C. Greubel, Sep 10 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 22*t + 252*t^16 - 231*t^17).
a(n) = 21*Sum_{j=1..15} a(n-j) - 231*a(n-16). (End)
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^16)/(1-22*t+252*t^16-231*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 10 2023 *)
coxG[{16, 231, -21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 27 2016 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-22*x+252*x^16-231*x^17) )); // G. C. Greubel, Sep 10 2023
(SageMath)
def A167937_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^16)/(1-22*x+252*x^16-231*x^17) ).list()
A167937_list(40) # G. C. Greubel, Sep 10 2023
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved