A168890 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = 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 21: a(21) = 2202009599999999999999999790, A170740(21) = 2202009600000000000000000000. - Klaus Brockhaus, Apr 05 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..15.

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, 19, 19, -190).

Formula

G.f.: (t^21 + 2*t^20 + 2*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^21 - 19*t^20 - 19*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).

Crossrefs

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

Sequence in context: A168746 A168794 A168842 * A168938 A168986 A169034

Adjacent sequences: A168887 A168888 A168889 * A168891 A168892 A168893

Keyword

nonn

Author

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

Status

approved