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Search: id:A157768
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| A157768 |
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a(n)=27225*n^2-39202*n+14112 (n>0) |
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+0
3
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| 2135, 44608, 141531, 292904, 498727, 759000, 1073723, 1442896, 1866519, 2344592, 2877115, 3464088, 4105511, 4801384, 5551707, 6356480, 7215703, 8129376, 9097499, 10120072, 11197095, 12328568, 13514491, 14754864, 16049687, 17398960
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OFFSET
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1,1
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COMMENT
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If A=[A157768] 27225*n.^2-39202*n +14112 (2135, 44608, 141531,.,); Y=[A157769] 8984250*n - 6468330 (2515920, 11500170, 20484420..,); X=[A157770] 1482401250*n^2-2134548900*n + 768398401 (116250751, 2428905601, 7706362951,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 116250751^2-2135 *2515920^2=1; 2428905601^2-44608*11500170^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=27225*n^2-39202*n+14112 (n>0)
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EXAMPLE
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For n=1, a(1)=2135; n=2, a(2)=44608; n=3, a(3)=141531
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CROSSREFS
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Cf. 157769, A157770
Sequence in context: A031544 A066817 A110024 this_sequence A067199 A064249 A020398
Adjacent sequences: A157765 A157766 A157767 this_sequence A157769 A157770 A157771
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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.i), Mar 06 2009
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