A166924 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676416, 77309411328, 618475290588, 4947802324416, 39582418593060, 316659348726336, 2533274789665536, 20266198316163072, 162129586520014848

Offset

0,2

Comments

The initial terms coincide with those of A003951, 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 (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).

Formula

G.f.: (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)/(28*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).

Mathematica

CoefficientList[Series[(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)/(28*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 28 2016 *)
coxG[{13, 28, -7}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 12 2023 *)

Prog

(PARI) Vec((1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12)*(1+x)/(1-7*x-7*x^2-7*x^3-7*x^4-7*x^5-7*x^6-7*x^7-7*x^8-7*x^9-7*x^10-7*x^11-7*x^12+28*x^13)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A003951, A154638.

Sequence in context: A165787 A166367 A166541 * A167110 A167658 A167900

Adjacent sequences: A166921 A166922 A166923 * A166925 A166926 A166927

Keyword

nonn,easy,changed

Author

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

Status

approved