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75, 303, 683, 1215, 1899, 2735, 3723, 4863, 6155, 7599, 9195, 10943, 12843, 14895, 17099, 19455, 21963, 24623, 27435, 30399, 33515, 36783, 40203, 43775, 47499, 51375, 55403, 59583, 63915, 68399, 73035, 77823, 82763, 87855, 93099, 98495
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (76*n^2-1)^2 - (1444*n^2-38) * (2*n)^2 = 1 can be written as
the Pell equation (a(n))^2 - A158764(n) * (A005843(n))^2 = 1.
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LINKS
| Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
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FORMULA
| a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: x*(-75-78*x+x^2)/(x-1)^3.
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MATHEMATICA
| 76*Range[40]^2-1 (* or *) LinearRecurrence[{3, -3, 1}, {75, 303, 683}, 40] (* From Harvey P. Dale, Jan 18 2012 *)
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CROSSREFS
| Cf. A005843, A158764
Sequence in context: A098230 A174685 A158742 * A055561 A193252 A015223
Adjacent sequences: A158762 A158763 A158764 * A158766 A158767 A158768
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 26 2009
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EXTENSIONS
| Comment rewritten and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009
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