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Search: id:A157375
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| A157375 |
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a(n)=2401*n^2-980*n+99 (n>0) |
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+0
3
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| 1520, 7743, 18768, 34595, 55224, 80655, 110888, 145923, 185760, 230399, 279840, 334083, 393128, 456975, 525624, 599075, 677328, 760383, 848240, 940899, 1038360, 1140623, 1247688, 1359555, 1476224, 1597695, 1723968, 1855043, 1990920
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OFFSET
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1,1
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COMMENT
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If A=[A157373] 49*n.^2-20*n +2 (31,158,383,706,...,); Y=[A157374] 343*n-70 (273, 616, 959, 1302,..,); X=[A157370] 2401*n^2-980*n+99 (1520,7743,18768,34595,.,) ; , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: 1520^2-31*273^2=1; 7743^2-158*616^2=1; 18768^2-383*959^2=1; 34595^2-706*1302^2=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)=2401*n^2-980*n+99 (n>0)
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EXAMPLE
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For n=1, a(1)=1520; n=2, a(2)=7743; n=3, a(3)=18768
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CROSSREFS
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Cf. A157373, A157374
Sequence in context: A031810 A020415 A112641 this_sequence A074906 A025413 A025410
Adjacent sequences: A157372 A157373 A157374 this_sequence A157376 A157377 A157378
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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), Feb 28 2009
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