A170556 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

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

Offset

0,2

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

Table of n, a(n) for n=0..15.

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, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).

Formula

G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*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)/(153*t^47 -

17*t^46 - 17*t^45 - 17*t^44 - 17*t^43 - 17*t^42 - 17*t^41 - 17*t^40 -

17*t^39 - 17*t^38 - 17*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)

Mathematica

With[{num=Total[2t^Range[46]]+t^47+1, den=Total[-17 t^Range[46]]+ 153t^47+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Apr 01 2012 *)

Crossrefs

Sequence in context: A170412 A170460 A170508 * A170604 A170652 A170700

Adjacent sequences: A170553 A170554 A170555 * A170557 A170558 A170559

Keyword

nonn

Author

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

Status

approved