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A094347
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a(n) = 14*a(n-1) - a(n-2); a(0) = a(1) = 2.
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6
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2, 2, 26, 362, 5042, 70226, 978122, 13623482, 189750626, 2642885282, 36810643322, 512706121226, 7141075053842, 99462344632562, 1385331749802026, 19295182152595802, 268747218386539202, 3743165875258953026
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OFFSET
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0,1
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COMMENTS
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Even x satisfying the Pellian x^2 - 3*y^2 = 1. For corresponding y see A028230.
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LINKS
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FORMULA
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a(n) = ((2 + sqrt(3))^(2*n - 1) + (2 - sqrt(3))^(2*n - 1))/2. - Gerry Martens, Jun 03 2015
a(n) = (1/2)*sqrt(4 + (-2*sqrt(-2 + (7 - 4*sqrt(3))^(2*n) + (7 + 4*sqrt(3))^(2*n)) + sqrt(3)*sqrt(2 + (7 - 4*sqrt(3))^(2*n) + (7 + 4*sqrt(3))^(2*n)))^2). - Gerry Martens, Jun 03 2015
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MATHEMATICA
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LinearRecurrence[{14, -1}, {2, 2}, 40] (* or *) CoefficientList[ Series[2(1-13x)/(1-14x+x^2), {x, 0, 39}], x] (* Harvey P. Dale, Apr 23 2011 *)
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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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STATUS
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approved
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