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Search: id:A158742
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| 1, 75, 297, 667, 1185, 1851, 2665, 3627, 4737, 5995, 7401, 8955, 10657, 12507, 14505, 16651, 18945, 21387, 23977, 26715, 29601, 32635, 35817, 39147, 42625, 46251, 50025, 53947, 58017, 62235, 66601, 71115, 75777, 80587, 85545, 90651, 95905
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The identity (74*n^2+1)^2 - (1369*n^2+37) * (2*n)^2 = 1 can be written as
the Pell equation (a(n))^2 - A158741(n) * (A005843(n))^2 = 1.
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LINKS
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Wolfram MathWorld, Pell Equation
Edward Everett Withford, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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FORMULA
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a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: -(1+72*x+75*x^2)/(x-1)^3.
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CROSSREFS
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Cf. A005843, A158741
Sequence in context: A044788 A003503 A098230 this_sequence A158765 A055561 A015223
Adjacent sequences: A158739 A158740 A158741 this_sequence A158743 A158744 A158745
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tn.it), Mar 25 2009
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EXTENSIONS
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Comment rewritten, a(0) added and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009
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