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A170731 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I. 1
1, 50, 2450, 120050, 5882450, 288240050, 14123762450, 692064360050, 33911153642450, 1661646528480050, 81420679895522450, 3989613314880600050, 195491052429149402450, 9579061569028320720050, 469374016882387715282450 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170769, 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 1225.  - Vincenzo Librandi, Dec 08 2012

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).

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)/(1176*t^50 - 48*t^49 - 48*t^48 - 48*t^47 - 48*t^46 - 48*t^45 -

48*t^44 - 48*t^43 - 48*t^42 - 48*t^41 - 48*t^40 - 48*t^39 - 48*t^38 -

48*t^37 - 48*t^36 - 48*t^35 - 48*t^34 - 48*t^33 - 48*t^32 - 48*t^31 -

48*t^30 - 48*t^29 - 48*t^28 - 48*t^27 - 48*t^26 - 48*t^25 - 48*t^24 -

48*t^23 - 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 - 48*t^18 - 48*t^17 -

48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 -

48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 -

48*t + 1)

MATHEMATICA

With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-48 t^Range[49]] + 1176t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Libramdi_, Dec 08 2012 *)

CROSSREFS

Sequence in context: A170587 A170635 A170683 * A170769 A218753 A120998

Adjacent sequences:  A170728 A170729 A170730 * A170732 A170733 A170734

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified May 16 06:54 EDT 2021. Contains 343939 sequences. (Running on oeis4.)