A167111 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283245, 228767924548800, 2058911320935600, 18530201888388000, 166771816995200400

Offset

0,2

Comments

The initial terms coincide with those of A003952, 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 (8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).

Formula

G.f.: (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)/(36*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

Mathematica

CoefficientList[Series[(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)/ (36*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 03 2016 *)

Prog

(PARI) first(n)=Vec((1+x^2+x^4+x^6+x^8+x^10+x^12)*(1+x)^2/(1-8*x-8*x^2-8*x^3-8*x^4-8*x^5-8*x^6-8*x^7-8*x^8-8*x^9-8*x^10-8*x^11-8*x^12-8*x^13+36*x^14)+O(x^(n+1))) \\ Charles R Greathouse IV, Jun 11 2026

Crossrefs

Cf. A003952, A154638.

Sequence in context: A166368 A166543 A166933 * A167659 A167908 A168687

Adjacent sequences: A167108 A167109 A167110 * A167112 A167113 A167114

Keyword

nonn,easy

Author

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

Status

approved