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Search: id:A158689
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| 1, 67, 265, 595, 1057, 1651, 2377, 3235, 4225, 5347, 6601, 7987, 9505, 11155, 12937, 14851, 16897, 19075, 21385, 23827, 26401, 29107, 31945, 34915, 38017, 41251, 44617, 48115, 51745, 55507, 59401, 63427, 67585, 71875, 76297, 80851, 85537
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OFFSET
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0,2
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COMMENT
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The identity (66*n^2+1)^2 - (1089*n^2+33) * (2*n)^2 = 1 can be written as
the Pell equation (a(n))^2 - A158688(n) * (A005843(n))^2 = 1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
Wolfram MathWorld, 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.: -(1+64*x+67*x^2)/(x-1)^3.
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CROSSREFS
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Cf. A005843, A158688
Sequence in context: A142273 A141985 A142429 this_sequence A142486 A158730 A140731
Adjacent sequences: A158686 A158687 A158688 this_sequence A158690 A158691 A158692
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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 24 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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