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Search: id:A158765
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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
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OFFSET
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1,1
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COMMENT
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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
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Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
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FORMULA
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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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CROSSREFS
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Cf. A005843, A158764
Adjacent sequences: A158762 A158763 A158764 this_sequence A158766 A158767 A158768
Sequence in context: A003503 A098230 A158742 this_sequence A055561 A015223 A129625
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KEYWORD
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nonn,easy,new
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 26 2009
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EXTENSIONS
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Comment rewritten and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009
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