A167107 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593750, 292968750, 1464843750, 7324218735, 36621093600, 183105467640, 915527336400, 4577636673000, 22888183320000, 114440916375000, 572204580750000

Offset

0,2

Comments

The initial terms coincide with those of A003948, 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 (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).

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

Prog

(PARI) Vec((1+x^2+x^4+x^6+x^8+x^10+x^12)*(1+x)^2/(1-4*x-4*x^2-4*x^3-4*x^4-4*x^5-4*x^6-4*x^7-4*x^8-4*x^9-4*x^10-4*x^11-4*x^12-4*x^13+10*x^14)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A003948, A154638.

Sequence in context: A166364 A166500 A166877 * A167651 A167897 A168683

Adjacent sequences: A167104 A167105 A167106 * A167108 A167109 A167110

Keyword

nonn,easy,changed

Author

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

Status

approved