A168718 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747904000000000, 429916160000000000, 17196646400000000000, 687865856000000000000, 27514634240000000000000

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170760, although the two sequences are eventually different.

First disagreement at index 17: a(17) = 1760936591359999999999999180, A170760(17) = 1760936591360000000000000000. - Klaus Brockhaus, Mar 28 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 (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).

Crossrefs

Cf. A170760 (G.f.: (1+x)/(1-40*x)).

Programs

Mathematica

CoefficientList[Series[(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)/(780*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 05 2016 *)
coxG[{17,780,-39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 10 2016 *)

Formula

G.f.: (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)/(780*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).