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A170687
Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
1
1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593750, 292968750, 1464843750, 7324218750, 36621093750, 183105468750, 915527343750, 4577636718750, 22888183593750, 114440917968750, 572204589843750
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003948, 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 15. - Vincenzo Librandi, Dec 09 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
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)/(10*t^50 - 4*t^49 - 4*t^48 - 4*t^47 - 4*t^46 - 4*t^45 - 4*t^44
- 4*t^43 - 4*t^42 - 4*t^41 - 4*t^40 - 4*t^39 - 4*t^38 - 4*t^37 - 4*t^36
- 4*t^35 - 4*t^34 - 4*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28
- 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20
- 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12
- 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 -
4*t^3 - 4*t^2 - 4*t + 1)
MATHEMATICA
With[{num=Total[2t^Range[49]]+t^50+1, den=Total[-4 t^Range[49]]+10t^50+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Mar 26 2012 *)
CROSSREFS
Sequence in context: A170543 A170591 A170639 * A003948 A105488 A252699
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved