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Search: id:A158741
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| 37, 1406, 5513, 12358, 21941, 34262, 49321, 67118, 87653, 110926, 136937, 165686, 197173, 231398, 268361, 308062, 350501, 395678, 443593, 494246, 547637, 603766, 662633, 724238, 788581, 855662, 925481, 998038, 1073333, 1151366, 1232137
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OFFSET
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0,1
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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 (A158742(n))^2 - a(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.: -37*(1+35*x+38*x^2)/(x-1)^3.
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CROSSREFS
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Cf. A005843, A158742
Sequence in context: A078303 A009981 A097315 this_sequence A094490 A009695 A130013
Adjacent sequences: A158738 A158739 A158740 this_sequence A158742 A158743 A158744
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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 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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