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Search: id:A158769
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| 1, 79, 313, 703, 1249, 1951, 2809, 3823, 4993, 6319, 7801, 9439, 11233, 13183, 15289, 17551, 19969, 22543, 25273, 28159, 31201, 34399, 37753, 41263, 44929, 48751, 52729, 56863, 61153, 65599, 70201, 74959, 79873, 84943, 90169, 95551, 101089
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OFFSET
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0,2
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COMMENT
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The identity (78*n^2+1)^2 - (1521*n^2+39) * (2*n)^2 = 1 can be written as
the Pell equation (a(n))^2 - A158768(n) * (A005843(n))^2 = 1.
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LINKS
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Edward Everett Withford, Pell Equation
Wolfram MathWorld, 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+76*x+79*x^2)/(x-1)^3.
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CROSSREFS
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Cf. A005843, A158768
Sequence in context: A141914 A142932 A082077 this_sequence A158774 A157507 A142897
Adjacent sequences: A158766 A158767 A158768 this_sequence A158770 A158771 A158772
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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)tin.it), Mar 26 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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