A170238 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = 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.

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, 35, 35, 35, 35, 35, 35, 35, 35, -630).

Formula

G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +

2*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^40 - 35*t^39 - 35*t^38 - 35*t^37 - 35*t^36 - 35*t^35 - 35*t^34

- 35*t^33 - 35*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)

Crossrefs

Sequence in context: A170094 A170142 A170190 * A170286 A170334 A170382

Adjacent sequences: A170235 A170236 A170237 * A170239 A170240 A170241

Keyword

nonn

Author

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

Status

approved