A166855 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297895272, 7329779811806298916608, 351829430966702345288856

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, -1128).

Formula

G.f.: (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^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^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^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, May 25 2016 *)

Prog

(PARI) Vec((1+x^4+x^8)*(1+x^2)*(1+x)^2/(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+1128*x^12)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A170768, A154638.

Sequence in context: A165709 A166324 A166443 * A167102 A167646 A167879

Adjacent sequences: A166852 A166853 A166854 * A166856 A166857 A166858

Keyword

nonn,easy

Author

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

Status

approved