A168816 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506306048, 54413821892871264854016

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170762, although the two sequences are eventually different.

First disagreement at index 19: a(19) = 7111409421007917621169651186809, A170762(19) = 7111409421007917621169651187712. - Klaus Brockhaus, Apr 01 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 (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

Crossrefs

Cf. A170762 (G.f.: (1+x)/(1-42*x)).

Programs

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)/(861*t^19 -41*t^18 -41*t^17 -41*t^16 -41*t^15 -41*t^14 - 41*t^13 -41*t^12 -41*t^11 -41*t^10 -41*t^9 -41*t^8 -41*t^7 -41*t^6 -41*t^5 - 41*t^4 -41*t^3 -41*t^2 -41*t +1), {t,0,50}], t] (* G. C. Greubel, Nov 21 2016 *)
coxG[{19,861,-41}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 17 2024 *)

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)/(861*t^19 - 41*t^18 - 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).