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.

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

G. C. Greubel, Table of n, a(n) for n = 0..740

Index entries for linear recurrences with constant coefficients, signature (20, 20, 20, 20, 20, -210).

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

Adjacent sequences: A163985 A163986 A163987 * A163989 A163990 A163991

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved