A166740 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429889152, 942237774900992, 43342937645445632, 1993775131690499072, 91713656057762956231, 4218828178657095936900, 194066096218226410811085

Offset

0,2

Comments

The initial terms coincide with those of A170766, 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 (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).

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)/(1035*t^12 - 45*t^11 - 45*t^10 - 45*t^9 -45*t^8 -45*t^7 -45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*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)/(1035*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*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/(1-45*x-45*x^2-45*x^3-45*x^4-45*x^5-45*x^6-45*x^7-45*x^8-45*x^9-45*x^10-45*x^11+1035*x^12)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A170766, A154638.

Sequence in context: A165703 A166308 A166441 * A167100 A167644 A167978

Adjacent sequences: A166737 A166738 A166739 * A166741 A166742 A166743

Keyword

nonn,easy

Author

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

Status

approved