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A145694
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Numbers Y such that 57*Y^2+19 is a square.
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1
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5, 1515, 457525, 138171035, 41727195045, 12601474732555, 3805603642036565, 1149279698420310075, 347078663319291606085, 104816607042727644727595, 31654268248240429416127605, 9559484194361566956025809115, 2886932572428944980290378225125
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n+2) = 302*a(n+1)-a(n).
G.f.: 5*x*(x+1) / (x^2-302*x+1). - Colin Barker, Oct 21 2014
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EXAMPLE
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a(1)=5 because the first relation is 38^2=57*5^2+19.
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MATHEMATICA
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CoefficientList[Series[5 (x + 1)/(x^2 - 302 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)
LinearRecurrence[{302, -1}, {5, 1515}, 15] (* Harvey P. Dale, Jun 25 2021 *)
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PROG
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(PARI) Vec(5*x*(x+1)/(x^2-302*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014
(Magma) I:=[5, 1515]; [n le 2 select I[n] else 302*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 21 2014
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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