login
A163988
Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
2
1, 22, 462, 9702, 203742, 4278582, 89849991, 1886844960, 39623642520, 832094358480, 17473936704840, 366951729513600, 7705966552789890, 161824882502745000, 3398313815357307000, 71364407061765925800
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170741, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(210*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
G.f.: (1+x)*(1-x^6)/(1 -21*x +230*x^6 -210*x^7). - G. C. Greubel, Apr 25 2019
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^6)/(1-21*x+230*x^6-210*x^7), {x, 0, 20}], x] (* G. C. Greubel, Aug 24 2017 *)
coxG[{6, 210, -20, 20}] (* The coxG program is at A169452 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-21*x+230*x^6-210*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)/(1-21*x+230*x^6-210*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-21*x+230*x^6-210*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
CROSSREFS
Sequence in context: A342887 A163149 A163514 * A164635 A164956 A165364
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved