A170076 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305856, 1221099791505408, 21979796247097344, 395636332447752192, 7121453984059539456

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170738, although the two sequences are eventually different.

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

Links

• Index entries for linear recurrences with constant coefficients, signature (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).

Formula

G.f. (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)/(153*t^37 - 17*t^36 - 17*t^35 -

17*t^34 - 17*t^33 - 17*t^32 - 17*t^31 - 17*t^30 - 17*t^29 - 17*t^28 -

17*t^27 - 17*t^26 - 17*t^25 - 17*t^24 - 17*t^23 - 17*t^22 - 17*t^21 -

17*t^20 - 17*t^19 - 17*t^18 - 17*t^17 - 17*t^16 - 17*t^15 - 17*t^14 -

17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 -

17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1)