A167933 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170740, 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..500
• Index entries for linear recurrences with constant coefficients, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Crossrefs

Cf. A154638, A170740.

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^16)/(1-20*x+209*x^16-190*x^17) )); // G. C. Greubel, Apr 25 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^16)/(1-20*x+209*x^16-190*x^17), {x, 0, 20}], x] (* G. C. Greubel, Jul 01 2016, modified Apr 25 2019 *)
coxG[{16, 190, -19, 20}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^16)/(1-20*x+209*x^16-190*x^17)) \\ G. C. Greubel, Apr 25 2019

Sage

((1+x)*(1-x^16)/(1-20*x+209*x^16-190*x^17)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

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)/( 190*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

G.f.: (1+x)*(1-x^16)/(1 -20*x +209*x^16 -190*x^17). - G. C. Greubel, Apr 25 2019