A170350 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836480, 85899345920, 343597383680, 1374389534720, 5497558138880, 21990232555520, 87960930222080

Offset

0,2

Comments

The initial terms coincide with those of A003947, 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..23.

Index entries for linear recurrences with constant coefficients, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).

Formula

G.f. (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)/(6*t^43 - 3*t^42 - 3*t^41 - 3*t^40 - 3*t^39 - 3*t^38

- 3*t^37 - 3*t^36 - 3*t^35 - 3*t^34 - 3*t^33 - 3*t^32 - 3*t^31 - 3*t^30

- 3*t^29 - 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22

- 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14

- 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 -

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

Mathematica

With[{num=Total[2t^Range[42]]+t^43+1, den=Total[-3 t^Range[42]]+6t^43+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Apr 03 2013 *)

Crossrefs

Sequence in context: A170206 A170254 A170302 * A170398 A170446 A170494

Adjacent sequences: A170347 A170348 A170349 * A170351 A170352 A170353

Keyword

nonn

Author

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

Status

approved