A166739 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152342715, 3171816083526855375600, 142731723758708489807160

Offset

0,2

Comments

The initial terms coincide with those of A170765, 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 (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).

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)/(990*t^12 - 44*t^11 - 44*t^10 - 44*t^9 -44*t^8 -44*t^7 -44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

Mathematica

coxG[{12, 990, -44}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 16 2015 *)
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)/(990*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 24 2016 *)

Prog

(PARI) Vec((1+x^4+x^8)*(1+x^2)*(1+x)^2/(1-44*x-44*x^2-44*x^3-44*x^4-44*x^5-44*x^6-44*x^7-44*x^8-44*x^9-44*x^10-44*x^11+990*x^12)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A170765, A154638.

Sequence in context: A165702 A166303 A166440 * A167099 A167643 A167861

Adjacent sequences: A166736 A166737 A166738 * A166740 A166741 A166742

Keyword

nonn,easy

Author

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

Status

approved