A167112 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 109999999999945, 1099999999998900, 10999999999983555, 109999999999781100

Offset

0,2

Comments

The initial terms coincide with those of A003953, 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 (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

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)/(45*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*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)/ (45*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*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/(1-9*x-9*x^2-9*x^3-9*x^4-9*x^5-9*x^6-9*x^7-9*x^8-9*x^9-9*x^10-9*x^11-9*x^12-9*x^13+45*x^14)+O(x^(n+1))) \\ Charles R Greathouse IV, Jun 13 2026

Crossrefs

Cf. A003953, A154638.

Sequence in context: A166369 A166551 A166950 * A167664 A167914 A003953

Adjacent sequences: A167109 A167110 A167111 * A167113 A167114 A167115

Keyword

nonn,easy

Author

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

Status

approved