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A004294
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Expansion of (1+2*x+x^2)/(1-34*x+x^2).
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1
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1, 36, 1224, 41580, 1412496, 47983284, 1630019160, 55372668156, 1881040698144, 63900011068740, 2170719335639016, 73740557400657804, 2505008232286726320, 85096539340348037076, 2890777329339546534264, 98201332658204234127900, 3335954533049604413814336
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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) = 3*((17+12*sqrt(2))^(1-n)*(-1+(17+12*sqrt(2))^(2*n)))/(48+34*sqrt(2)) for n>0.
a(n) = 34*a(n-1) - a(n-2) for n>2.
(End)
a(n) = (-(-1)^(2^n) + 3*sqrt(2)*sinh(n*log(17+12*sqrt(2))) + 1)/2. - Ilya Gutkovskiy, Apr 16 2016
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MATHEMATICA
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CoefficientList[Series[(1+2*x+x^2)/(1-34*x+x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 14 2012 *)
LinearRecurrence[{34, -1}, {1, 36, 1224}, 20] (* Harvey P. Dale, Mar 29 2019 *)
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PROG
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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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