A166969 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885886, 25090245516518, 326173191714643, 4240251492289176, 55123269399744000, 716602502196473256

Offset

0,2

Comments

The initial terms coincide with those of A170733, 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 (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).

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)/(78*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*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)/(78*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 29 2016 *)
coxG[{13, 78, -12}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 11 2020 *)

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)/(1-12*x-12*x^2-12*x^3-12*x^4-12*x^5-12*x^6-12*x^7-12*x^8-12*x^9-12*x^10-12*x^11-12*x^12+78*x^13)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A170733, A154638.

Sequence in context: A165874 A166379 A166568 * A167115 A167670 A167922

Adjacent sequences: A166966 A166967 A166968 * A166970 A166971 A166972

Keyword

nonn,easy,changed

Author

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

Status

approved