A170184 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305190000000000, 549155700000000000, 16474671000000000000, 494240130000000000000, 14827203900000000000000

Offset

0,2

Comments

The initial terms coincide with those of A170750, 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..15.

Index entries for linear recurrences with constant coefficients, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).

Formula

G.f. (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)/(435*t^39 -

29*t^38 - 29*t^37 - 29*t^36 - 29*t^35 - 29*t^34 - 29*t^33 - 29*t^32 -

29*t^31 - 29*t^30 - 29*t^29 - 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 -

29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 -

29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 -

29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 -

29*t^2 - 29*t + 1)

Mathematica

coxG[{39, 435, -29}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 13 2015 *)

Crossrefs

Sequence in context: A170040 A170088 A170136 * A170232 A170280 A170328

Adjacent sequences: A170181 A170182 A170183 * A170185 A170186 A170187

Keyword

nonn

Author

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

Status

approved