A167396 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910946, 1449027061218, 47817893020194, 1577990469666402, 52073685498991266, 1718431621466711778, 56708243508401488674, 1871372035777249125681, 61755277180649221128960

Offset

0,2

Comments

The initial terms coincide with those of A170753, 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 (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).

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)/(528*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).

Mathematica

coxG[{14, 528, -32}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 25 2015 *)
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)/ (528*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 12 2016 *)

Prog

(PARI) first(n)=Vec((1+x^2+x^4+x^6+x^8+x^10+x^12)*(1+x)^2/(1-32*x-32*x^2-32*x^3-32*x^4-32*x^5-32*x^6-32*x^7-32*x^8-32*x^9-32*x^10-32*x^11-32*x^12-32*x^13+528*x^14)+O(x^(n+1))) \\ Charles R Greathouse IV, Jun 11 2026

Crossrefs

Cf. A170753, A154638.

Sequence in context: A166428 A166682 A167087 * A167785 A167950 A168711

Adjacent sequences: A167393 A167394 A167395 * A167397 A167398 A167399

Keyword

nonn,easy

Author

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

Status

approved