A167652 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263232, 2539579392, 15237476352, 91424858112, 548549148651, 3291294891780, 19747769349945, 118486616095260, 710919696545100, 4265518179111840

Offset

0,2

Comments

The initial terms coincide with those of A003949, 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 (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).

Formula

G.f.: (t^15 + 2*t^14 + 2*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)/(15*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).

Mathematica

CoefficientList[Series[(t^15 + 2*t^14 + 2*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)/(15*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 18 2016 *)

Prog

(PARI) first(n)=Vec((1+x^5+x^10)*(1+x+x^2+x^3+x^4)*(1+x)/(1-5*x-5*x^2-5*x^3-5*x^4-5*x^5-5*x^6-5*x^7-5*x^8-5*x^9-5*x^10-5*x^11-5*x^12-5*x^13-5*x^14+15*x^15)+O(x^(n+1))) \\ Charles R Greathouse IV, Jun 12 2026

Crossrefs

Cf. A003949, A154638.

Sequence in context: A166518 A166878 A167108 * A167898 A168684 A168732

Adjacent sequences: A167649 A167650 A167651 * A167653 A167654 A167655

Keyword

nonn,easy

Author

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

Status

approved