A167096 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506305145, 54413821892871264778164

Offset

0,2

Comments

The initial terms coincide with those of A170762, 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 (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

Formula

G.f.: (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^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).

Mathematica

CoefficientList[Series[(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^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, Jun 02 2016 *)

Prog

(PARI) Vec((1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12)*(1+x)/(1-41*x-41*x^2-41*x^3-41*x^4-41*x^5-41*x^6-41*x^7-41*x^8-41*x^9-41*x^10-41*x^11-41*x^12+861*x^13)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A170762, A154638.

Sequence in context: A166233 A166437 A166717 * A167640 A167849 A167959

Adjacent sequences: A167093 A167094 A167095 * A167097 A167098 A167099

Keyword

nonn,easy

Author

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

Status

approved