A168906 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = 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 21: a(21) = 494597297937218160510037301132646, A170756(21) = 494597297937218160510037301133312. - Klaus Brockhaus, Apr 05 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, -630).

Formula

G.f.: (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^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

coxG[{21, 630, -35}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 04 2022 *)

Crossrefs

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

Sequence in context: A168762 A168810 A168858 * A168954 A169002 A169050

Adjacent sequences: A168903 A168904 A168905 * A168907 A168908 A168909

Keyword

nonn

Author

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

Status

approved