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A170679
Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
0
1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170765, although the two sequences are eventually different.
First disagreement is at index 49, the difference is 1035. - Klaus Brockhaus, Jun 14 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).
FORMULA
G.f.: (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)/(990*t^49 - 44*t^48 - 44*t^47 - 44*t^46 - 44*t^45 - 44*t^44 - 44*t^43 - 44*t^42 - 44*t^41 - 44*t^40 - 44*t^39 - 44*t^38 - 44*t^37 - 44*t^36 - 44*t^35 - 44*t^34 - 44*t^33 - 44*t^32 - 44*t^31 - 44*t^30 - 44*t^29 - 44*t^28 - 44*t^27 - 44*t^26 - 44*t^25 - 44*t^24 - 44*t^23 - 44*t^22 - 44*t^21 - 44*t^20 - 44*t^19 - 44*t^18 - 44*t^17 - 44*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
MATHEMATICA
With[{num=Total[2t^Range[48]]+t^49+1, den=Total[-44 t^Range[48]]+1+ 990t^49}, CoefficientList[Series[num/den, {t, 0, 21}], t]] (* Harvey P. Dale, Jun 14 2011 *)
CROSSREFS
Cf. A170765 (G.f.: (1+x)/(1-45*x)).
Sequence in context: A170535 A170583 A170631 * A170727 A170765 A218748
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved