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A162959
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The pairs (x,y) such that (x^2 + y^2)/(x*y + 1) is a perfect square, i.e., 4.
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1
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0, 2, 2, 8, 8, 30, 30, 112, 112, 418, 418, 1560, 1560, 5822, 5822, 21728, 21728, 81090, 81090, 302632, 302632, 1129438, 1129438, 4215120, 4215120, 15731042, 15731042, 58709048, 58709048, 219105150, 219105150, 817711552, 817711552, 3051741058, 3051741058, 11389252680, 11389252680
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 4*a(n-2) - a(n-4).
G.f.: 2*x^2*(x+1) / (x^4-4*x^2+1). (End)
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EXAMPLE
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Pairs are (8,30) with (8^2 + 30^2)/(8*30 + 1) = 4, or (30,112) with (30^2 + 112^2)/(30*112 + 1) = 4.
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MATHEMATICA
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CoefficientList[Series[2 x (x + 1) / (x^4 - 4 x^2 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, May 14 2013 *)
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PROG
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(PARI) x='x+O('x^66); concat([0], Vec(2*x^2*(x+1)/(x^4-4*x^2+1))) \\ Joerg Arndt, May 15 2013
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CROSSREFS
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KEYWORD
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nonn,less,easy
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AUTHOR
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STATUS
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approved
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