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A163991
Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
2
1, 23, 506, 11132, 244904, 5387888, 118533283, 2607726660, 57369864321, 1262134326684, 27766896042732, 610870411765152, 13439120433048156, 295660019761129485, 6504506579923898238, 143098839952914095019, 3148167773259336785958, 69259543486514630343864
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.
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).
G.f.: (1+x)*(1-x^6)/(1 -22*x +252*x^6 -231*x^7). - G. C. Greubel, Apr 25 2019
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7), {x, 0, 20}], x] (* G. C. Greubel, Aug 24 2017, modified Apr 25 2019 *)
coxG[{6, 231, -21}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7)) \\ G. C. Greubel, Aug 24 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
CROSSREFS
Sequence in context: A212336 A163171 A163518 * A164636 A164957 A165365
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved