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A093328
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a(n) = 2*n^2 + 3.
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16
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3, 5, 11, 21, 35, 53, 75, 101, 131, 165, 203, 245, 291, 341, 395, 453, 515, 581, 651, 725, 803, 885, 971, 1061, 1155, 1253, 1355, 1461, 1571, 1685, 1803, 1925, 2051, 2181, 2315, 2453, 2595, 2741, 2891, 3045, 3203, 3365, 3531, 3701, 3875, 4053, 4235
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OFFSET
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0,1
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COMMENTS
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Number of 132-avoiding two-stack sortable permutations which also avoid 4321.
Conjecture: no perfect powers. - Zak Seidov, Sep 27 2015
Numbers k such that 2*k - 6 is a square. - Bruno Berselli, Nov 08 2017
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LINKS
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FORMULA
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G.f.: (3 - 4*x + 5*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=0} 1/a(n) = (1 + sqrt(3/2)*Pi*coth(sqrt(3/2)*Pi))/6. - Amiram Eldar, Nov 25 2020
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MATHEMATICA
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CoefficientList[Series[(3 - 4 x + 5 x^2)/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 08 2012 *)
LinearRecurrence[{3, -3, 1}, {3, 5, 11}, 50] (* Harvey P. Dale, Apr 03 2016 *)
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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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EXTENSIONS
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Simpler definition and new offset from Paul F. Brewbaker, Jun 23 2009
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STATUS
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approved
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