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Search: id:A157909
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| 72, 315, 720, 1287, 2016, 2907, 3960, 5175, 6552, 8091, 9792, 11655, 13680, 15867, 18216, 20727, 23400, 26235, 29232, 32391, 35712, 39195, 42840, 46647, 50616, 54747, 59040, 63495, 68112, 72891, 77832, 82935, 88200, 93627, 99216, 104967
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OFFSET
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1,1
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COMMENT
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If A=[A157909] 81*n.^2-9 (72,315,720,.,); Y=[A005843] 2*n (n>0, 2,4,6,8,.,); X=[A157910] 18*n^2-1 (17, 71, 161,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 17^2-72 *2^2=1; 71^2-315*4^2=1; 161^2-720*6^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Philippe Chevanne, Pell Equation
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FORMULA
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a(n)=81*n^2-9 (n>0)
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EXAMPLE
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For n=1, a(1)=72; n=2, a(2)=315; n=3, a(3)=720
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CROSSREFS
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Cf. A005843, A157910
Sequence in context: A158488 A165139 A004007 this_sequence A107314 A090788 A084479
Adjacent sequences: A157906 A157907 A157908 this_sequence A157910 A157911 A157912
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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 09 2009
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