A170331 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910946, 1449027061218, 47817893020194, 1577990469666402, 52073685498991266, 1718431621466711778, 56708243508401488674, 1871372035777249126242, 61755277180649221165986

Offset

0,2

Comments

The initial terms coincide with those of A170753, 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 (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).

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)/(528*t^42 - 32*t^41 - 32*t^40 - 32*t^39 - 32*t^38 - 32*t^37 -

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

32*t^29 - 32*t^28 - 32*t^27 - 32*t^26 - 32*t^25 - 32*t^24 - 32*t^23 -

32*t^22 - 32*t^21 - 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 - 32*t^16 -

32*t^15 - 32*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 -

32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1)

Mathematica

With[{num=Total[2t^Range[41]]+t^42+1, den=Total[-32 t^Range[41]]+528t^42+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Apr 10 2014 *)
coxG[{42, 528, -32}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 05 2021 *)

Crossrefs

Sequence in context: A170187 A170235 A170283 * A170379 A170427 A170475

Adjacent sequences: A170328 A170329 A170330 * A170332 A170333 A170334

Keyword

nonn

Author

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

Status

approved