A167114 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818944, 115909305827328, 1390911669927858, 16690940039133360, 200291280469589166

Offset

0,2

Comments

The initial terms coincide with those of A170732, 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 (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).

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)/(66*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).

Mathematica

coxG[{14, 66, -11}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 25 2016 *)
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)/ (66*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*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/(1-11*x-11*x^2-11*x^3-11*x^4-11*x^5-11*x^6-11*x^7-11*x^8-11*x^9-11*x^10-11*x^11-11*x^12-11*x^13+66*x^14)+O(x^(n+1))) \\ Charles R Greathouse IV, Jun 11 2026

Crossrefs

Cf. A170732, A154638.

Sequence in context: A166377 A166558 A166954 * A167669 A167919 A168690

Adjacent sequences: A167111 A167112 A167113 * A167115 A167116 A167117

Keyword

nonn,easy

Author

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

Status

approved