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

0,2

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).

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).

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 *)

Crossrefs

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

Sequence in context: A168876 A168924 A168972 * A169068 A169116 A169164

Adjacent sequences: A169017 A169018 A169019 * A169021 A169022 A169023

Keyword

nonn

Author

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

Status

approved