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Search: id:A157653
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| A157653 |
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a(n)=80000*n^2-39200*n+4801 (n>0) |
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+0
3
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| 45601, 246401, 607201, 1128001, 1808801, 2649601, 3650401, 4811201, 6132001, 7612801, 9253601, 11054401, 13015201, 15136001, 17416801, 19857601, 22458401, 25219201, 28140001, 31220801, 34461601, 37862401, 41423201, 45144001
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If A=[A157651] 100*n.^2-49*n +6 (57, 308, 759, 1410 ,..,); Y=[A157627] 8000*n-1960 (6040, 14040, 22040..,); X=[A157628] 80000*n^2-39200*n+4801 (45601, 246401, 607201,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 45601^2-57*6040^2=1; 246401^2-308*14040^2=1; 607201^2-759*22040^2=1.
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LINKS
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Philippe Chevanne, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=80000*n^2-39200*n+4801 (n>0)
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EXAMPLE
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For n=1, a(1)=45601; n=2, a(2)=246401; n=3, a(3)=607201
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CROSSREFS
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Cf. A157651, A157652
Sequence in context: A031851 A163816 A055355 this_sequence A031841 A159725 A061405
Adjacent sequences: A157650 A157651 A157652 this_sequence A157654 A157655 A157656
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 03 2009
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