A169050 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575872, 3757718396731392, 135277862282330112, 4870003042163884032, 175320109517899825152, 6311523942644393705472

Offset

0,2

Comments

The initial terms coincide with those of A170756, although the two sequences are eventually different.

First disagreement at index 24: a(24) = 23075931532558850496756300321675804006, A170756(24) = 23075931532558850496756300321675804672. - Klaus Brockhaus, Apr 20 2011

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

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).

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)/(630*t^24 - 35*t^23 - 35*t^22 - 35*t^21 - 35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).

Mathematica

With[{num=Total[2t^Range[23]]+t^24+1, den=Total[-35 t^Range[23]]+630t^24+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Dec 12 2011 *)

Crossrefs

Cf. A170756 (G.f.: (1+x)/(1-36*x)).

Sequence in context: A168906 A168954 A169002 * A169098 A169146 A169194

Adjacent sequences: A169047 A169048 A169049 * A169051 A169052 A169053

Keyword

nonn

Author

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

Status

approved