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Search: id:A157665
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| A157665 |
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a(n)=729*n^2-1016*n+354 (n>0) |
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+0
3
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| 67, 1238, 3867, 7954, 13499, 20502, 28963, 38882, 50259, 63094, 77387, 93138, 110347, 129014, 149139, 170722, 193763, 218262, 244219, 271634, 300507, 330838, 362627, 395874, 430579, 466742, 504363, 543442, 583979, 625974, 669427, 714338
(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=[A157665] 729*n.^2-1016*n+354 (67, 1238, 3867, ,..,); Y=[A157666] 19683*n-13716 (5967, 25650, 45333,..,); X=[A157667] 531441*n^2-740664*n+258065 (48842, 902501, 2819042,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 48842^2-67*5967^2=1; 902501^2-1238*25650^2=1; 2819042^2-3867*45333^2=1.
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LINKS
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Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Philippe Chevanne, Pell Equation
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FORMULA
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a(n)=729*n^2-1016*n+354 (n>0)
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EXAMPLE
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For n=1, a(1)=67; n=2, a(2)=1238; n=, a(3)=3867
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CROSSREFS
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Cf. A157666, A157667
Sequence in context: A166802 A093267 A032651 this_sequence A078850 A092795 A017783
Adjacent sequences: A157662 A157663 A157664 this_sequence A157666 A157667 A157668
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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 04 2009
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