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A170728
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Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
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1
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1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429889152, 942237774900992, 43342937645445632, 1993775131690499072, 91713656057762957312, 4218828178657096036352, 194066096218226417672192
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OFFSET
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0,2
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COMMENTS
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The initial terms coincide with those of A170766, 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 1081. - Vincenzo Librandi, Dec 08 2012
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
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FORMULA
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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)/(1035*t^50 - 45*t^49 - 45*t^48 - 45*t^47 - 45*t^46 - 45*t^45 -
45*t^44 - 45*t^43 - 45*t^42 - 45*t^41 - 45*t^40 - 45*t^39 - 45*t^38 -
45*t^37 - 45*t^36 - 45*t^35 - 45*t^34 - 45*t^33 - 45*t^32 - 45*t^31 -
45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 -
45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 -
45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 -
45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 -
45*t + 1)
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MATHEMATICA
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With[{num=Total[2t^Range[49]]+t^50+1, den=Total[-45 t^Range[49]]+ 1035t^50+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Apr 18 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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