A170686 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = 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, 351843720888320, 1407374883553280

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.

About the initial comment, first disagreement is at index 50 and the difference is 10. - Vincenzo Librandi, Dec 09 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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, 3, 3, 3, 3, 3, 3, 3, -6).

Formula

G.f.: (t^50 + 2*t^49 + 2*t^48 + 2*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)/(6*t^50 - 3*t^49 - 3*t^48 - 3*t^47 - 3*t^46 - 3*t^45 - 3*t^44 -

3*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[2 t^Range[49]] + t^50 + 1, den = Total[-3 t^Range[49]] + 6 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 40}], t]] (* Vincenzo Librandi, Dec 09 2012 *)

Crossrefs

Sequence in context: A170590 A003947 A170638 * A369837 A363508 A252698

Adjacent sequences: A170683 A170684 A170685 * A170687 A170688 A170689

Keyword

nonn,easy,changed

Author

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

Status

approved