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A158688
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a(n)=33*(33*n^2+1).
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1
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33, 1122, 4389, 9834, 17457, 27258, 39237, 53394, 69729, 88242, 108933, 131802, 156849, 184074, 213477, 245058, 278817, 314754, 352869, 393162, 435633, 480282, 527109, 576114, 627297, 680658, 736197, 793914, 853809, 915882, 980133, 1046562
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The identity (66*n^2+1)^2 - (1089*n^2+33) * (2*n)^2 = 1 can be written as
the Pell equation (A158689(n))^2 - a(n) * (A005843(n))^2 = 1.
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LINKS
| Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
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FORMULA
| a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: -33*(1+31*x+34*x^2)/(x-1)^3.
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CROSSREFS
| Cf. A158689, A005843
Sequence in context: A187539 A130835 A077420 * A065424 A071268 A012805
Adjacent sequences: A158685 A158686 A158687 * A158689 A158690 A158691
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 24 2009
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EXTENSIONS
| Comment rewritten, a(0) added and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009
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