A170312 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544960, 850408685629440, 11905721598812160, 166680102383370240, 2333521433367183360

Offset

0,2

Comments

The initial terms coincide with those of A170734, 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..16.

Index entries for linear recurrences with constant coefficients, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).

Formula

G.f. (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)/(91*t^42 - 13*t^41 - 13*t^40 - 13*t^39 - 13*t^38 - 13*t^37 -

13*t^36 - 13*t^35 - 13*t^34 - 13*t^33 - 13*t^32 - 13*t^31 - 13*t^30 -

13*t^29 - 13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 - 13*t^23 -

13*t^22 - 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 -

13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 -

13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1)

Mathematica

With[{num=Total[2t^Range[41]]+t^42+1, den=Total[-13 t^Range[41]]+ 91t^42+1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Oct 11 2011 *)
coxG[{42, 91, -13}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 19 2025 *)

Crossrefs

Sequence in context: A170168 A170216 A170264 * A170360 A170408 A170456

Adjacent sequences: A170309 A170310 A170311 * A170313 A170314 A170315

Keyword

nonn

Author

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

Status

approved