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URL: https://oeis.org/A166610

⇱ A166610 - OEIS

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A166610
Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
7
1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460291, 295665060514120836, 6504631331310536193, 143101889288829107868
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, -231).
FORMULA
G.f.: (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^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).
G.f.: (1+x)*(1-x^12)/(1 -22*x + 252*x^12 - 231*x^13). - G. C. Greubel, Apr 25 2019
MATHEMATICA
coxG[{12, 231, -21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 03 2015 *)
CoefficientList[Series[(1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13), {x, 0, 20}], x] (* G. C. Greubel, May 18 2016, modified Apr 25 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)) \\ G. C. Greubel, Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13) )); // G. C. Greubel, Apr 25 2019
(SageMath) ((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
CROSSREFS
Sequence in context: A165365 A165939 A166417 * A167076 A167174 A167694
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved