A169020 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263232, 2539579392, 15237476352, 91424858112, 548549148672, 3291294892032, 19747769352192, 118486616113152, 710919696678912, 4265518180073472

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003949, although the two sequences are eventually different.

First disagreement at index 24: a(24) = 5528111561375219691, A003949(24) = 5528111561375219712. - Klaus Brockhaus, Apr 20 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).

Crossrefs

Cf. A003949 (G.f.: (1+x)/(1-6*x)).

Programs

Mathematica

With[{num=Total[2t^Range[23]]+t^24+1,den=Total[-5 t^Range[23]]+15t^24+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Jun 29 2014 *)

Formula

G.f.: (t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*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)/(15*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).