A169133 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416

Offset

0,2

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.

First disagreement at index 26: a(26) = 265098421726069091188171497832558356, A170743(26) = 265098421726069091188171497832558632. - Klaus Brockhaus, Apr 30 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 (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).

Formula

G.f.: (t^26 + 2*t^25 + 2*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)/(253*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

Mathematica

With[{num=Total[2t^Range[25]]+t^26+1, den=Total[-22 t^Range[25]]+ 253t^26+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Feb 27 2012 *)

Crossrefs

Cf. A170743 (G.f.: (1+x)/(1-23*x)).

Sequence in context: A168989 A169037 A169085 * A169181 A169229 A169277

Adjacent sequences: A169130 A169131 A169132 * A169134 A169135 A169136

Keyword

nonn

Author

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

Status

approved