A168794 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

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

Offset

0,2

Comments

The initial terms coincide with those of A170740, although the two sequences are eventually different.

First disagreement at index 19: a(19) = 5505023999999999999999790, A170740(19) = 5505024000000000000000000. - Klaus Brockhaus, Mar 30 2011

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, 19, 19, 19, -190).

Formula

G.f.: (t^19 + 2*t^18 + 2*t^17 + 2*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^19 - 19*t^18 - 19*t^17 - 19*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).

Mathematica

CoefficientList[Series[(t^19 + 2*t^18 + 2*t^17 + 2*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^19 - 19*t^18 - 19*t^17 - 19*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), {t, 0, 50}], t] (* G. C. Greubel, Aug 15 2016 *)

Crossrefs

Cf. A170740 (G.f.: (1+x)/(1-20*x)).

Sequence in context: A167933 A168698 A168746 * A168842 A168890 A168938

Adjacent sequences: A168791 A168792 A168793 * A168795 A168796 A168797

Keyword

nonn

Author

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

Status

approved