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Search: id:A157628
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| A157628 |
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a(n)=80000*n^2-120800*n+45601 (n>0) |
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+0
6
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| 4801, 124001, 403201, 842401, 1441601, 2200801, 3120001, 4199201, 5438401, 6837601, 8396801, 10116001, 11995201, 14034401, 16233601, 18592801, 21112001, 23791201, 26630401, 29629601, 32788801, 36108001, 39587201, 43226401
(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=[A157626] 100*n.^2-151*n +57 (6, 155, 504 ,..,); Y=[A157627] 8000*n-6040 (1960, 9960, 17960..,); X=[A157628] 80000*n^2-120800*n+45601 (4801, 124001, 403201,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 4801^2-6*1960^2=1; 124001^2-155*9960^2=1; 403201^2-504*17960^2=1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=80000*n^2-120800*n+45601 (n>0)
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EXAMPLE
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For n=1, a(1)=4801; n=2, a(2)=124001; n=3, a(3)=403201
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CROSSREFS
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Cf. A157626, A157627
Sequence in context: A096517 A096790 A157516 this_sequence A085322 A035786 A108010
Adjacent sequences: A157625 A157626 A157627 this_sequence A157629 A157630 A157631
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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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