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A170698 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I. 1
1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104512, 18691697672192, 299067162755072, 4785074604081152, 76561193665298432, 1224979098644774912, 19599665578316398592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170736, 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 136.  - 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 (15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, -120).

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)/(120*t^50 - 15*t^49 - 15*t^48 - 15*t^47 - 15*t^46 - 15*t^45 -

15*t^44 - 15*t^43 - 15*t^42 - 15*t^41 - 15*t^40 - 15*t^39 - 15*t^38 -

15*t^37 - 15*t^36 - 15*t^35 - 15*t^34 - 15*t^33 - 15*t^32 - 15*t^31 -

15*t^30 - 15*t^29 - 15*t^28 - 15*t^27 - 15*t^26 - 15*t^25 - 15*t^24 -

15*t^23 - 15*t^22 - 15*t^21 - 15*t^20 - 15*t^19 - 15*t^18 - 15*t^17 -

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

15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 -

15*t + 1).

MATHEMATICA

With[{num=Total[2 t^Range[49]] + t^50 + 1, den=Total[-15 t^Range[49]] + 120 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Dec 02 2012 *)

CROSSREFS

Sequence in context: A170554 A170602 A170650 * A170736 A131865 A298373

Adjacent sequences:  A170695 A170696 A170697 * A170699 A170700 A170701

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 19 03:15 EDT 2019. Contains 328211 sequences. (Running on oeis4.)