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Search: id:A158056
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| 18, 68, 150, 264, 410, 588, 798, 1040, 1314, 1620, 1958, 2328, 2730, 3164, 3630, 4128, 4658, 5220, 5814, 6440, 7098, 7788, 8510, 9264, 10050, 10868, 11718, 12600, 13514, 14460, 15438, 16448, 17490, 18564, 19670, 20808, 21978, 23180, 24414, 25680
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OFFSET
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1,1
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COMMENT
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If A=[A158056] 16*n.^2+2*n (n>0, 18, 68, 150,., ,.,); Y=[A010709] 4 (4,4,4, ,..,); X=[A158057] 16*n+1 (n>0, 17, 33, 49, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 17^2-18*4^2=1; 33^2-68*4^2=1; 49^2-150*4^2=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)=16*n^2+2*n (n>0)
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EXAMPLE
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For n=1, a(1)=18; n=2, a(2)=68; n=3, a(3)=150
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CROSSREFS
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Cf. A010709, A158057
Sequence in context: A143859 A063523 A045234 this_sequence A135470 A059224 A088490
Adjacent sequences: A158053 A158054 A158055 this_sequence A158057 A158058 A158059
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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 12 2009
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