A167102 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299028328, 351829430966702353303296

Offset

0,2

Comments

The initial terms coincide with those of A170768, 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 (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).

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)/(1128*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*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)/(1128*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 03 2016 *)
coxG[{13, 1128, -47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 16 2021 *)

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)/(1-47*x-47*x^2-47*x^3-47*x^4-47*x^5-47*x^6-47*x^7-47*x^8-47*x^9-47*x^10-47*x^11-47*x^12+1128*x^13)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A170768, A154638.

Sequence in context: A166324 A166443 A166855 * A167646 A167879 A167988

Adjacent sequences: A167099 A167100 A167101 * A167103 A167104 A167105

Keyword

nonn,easy

Author

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

Status

approved