A170194 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747904000000000, 429916160000000000, 17196646400000000000, 687865856000000000000, 27514634240000000000000

Offset

0,2

Comments

The initial terms coincide with those of A170760, 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 (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).

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)/(780*t^39 -

39*t^38 - 39*t^37 - 39*t^36 - 39*t^35 - 39*t^34 - 39*t^33 - 39*t^32 -

39*t^31 - 39*t^30 - 39*t^29 - 39*t^28 - 39*t^27 - 39*t^26 - 39*t^25 -

39*t^24 - 39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 - 39*t^19 - 39*t^18 -

39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 -

39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 -

39*t^2 - 39*t + 1)

Crossrefs

Sequence in context: A170050 A170098 A170146 * A170242 A170290 A170338

Adjacent sequences: A170191 A170192 A170193 * A170195 A170196 A170197

Keyword

nonn

Author

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

Status

approved