A169434 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = 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 is at index 32, the difference is 666. - Klaus Brockhaus, Jun 30 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, 35, 35, 35, 35, 35, 35, 35, 35, -630).

Formula

G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*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)/(630*t^32 - 35*t^31 - 35*t^30 - 35*t^29 - 35*t^28 - 35*t^27 - 35*t^26 - 35*t^25 - 35*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).

G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-35*sum(k=1..31,x^k)+630*x^32).

Mathematica

With[{num=Total[2t^Range[31]]+t^32+1, den=Total[-35 t^Range[31]]+ 630t^32+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Oct 03 2012 *)

Crossrefs

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

Sequence in context: A169290 A169338 A169386 * A169482 A169530 A169578

Adjacent sequences: A169431 A169432 A169433 * A169435 A169436 A169437

Keyword

nonn

Author

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

Status

approved