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Search: id:A158443
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| 12, 60, 140, 252, 396, 572, 780, 1020, 1292, 1596, 1932, 2300, 2700, 3132, 3596, 4092, 4620, 5180, 5772, 6396, 7052, 7740, 8460, 9212, 9996, 10812, 11660, 12540, 13452, 14396, 15372, 16380, 17420, 18492, 19596, 20732, 21900, 23100, 24332, 25596
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OFFSET
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1,1
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COMMENT
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If A=[A158443] 16*n.^2-4 (n>0, 12, 60,140,.,); Y=[A005843] 2*n (n>0, 2, 4, 6,.,); X=[A157914] 8*n^2-1 (n>0, 7, 31, 71, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 7^2-12*2^2=1; 31^2-60*4^2=1; 71^2-140*6^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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FORMULA
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a(n)=16*n^2-4 (n>0)
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EXAMPLE
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For n=1, a(1)=12; n=2, a(2)=60; n=3, a(3)=140
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CROSSREFS
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Cf. A157914, A005843
Sequence in context: A120644 A099829 A099830 this_sequence A153792 A000141 A008530
Adjacent sequences: A158440 A158441 A158442 this_sequence A158444 A158445 A158446
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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 19 2009
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