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A004298
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Expansion of (1+2*x+x^2)/(1-66*x+x^2).
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1
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1, 68, 4488, 296140, 19540752, 1289393492, 85080429720, 5614018968028, 370440171460128, 24443437297400420, 1612896421456967592, 106426720378862460652, 7022550648583465435440, 463381916086129856278388, 30576183911035987048938168, 2017564756212289015373640700
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OFFSET
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0,2
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REFERENCES
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P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.
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LINKS
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FORMULA
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a(n) = (sqrt(17)*(33+8*sqrt(17))^(-n)*(-1+(33+8*sqrt(17))^(2*n)))/4 for n>0.
a(n) = 66*a(n-1) - a(n-2) for n>2.
(End)
a(n) = (-(-1)^(2^n) + sqrt(17)*sinh(n*log(33+8*sqrt(17))) + 1)/2. - Ilya Gutkovskiy, Apr 16 2016
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MATHEMATICA
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CoefficientList[Series[(1+2*x+x^2)/(1-66*x+x^2), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 25 2012 *)
LinearRecurrence[{66, -1}, {1, 68, 4488}, 20] (* Harvey P. Dale, Sep 23 2020 *)
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PROG
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(PARI) Vec((1+2*x+x^2)/(1-66*x+x^2) + O(x^50)) \\ Colin Barker, Apr 16 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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