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A041060
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Numerators of continued fraction convergents to sqrt(37).
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1
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6, 73, 882, 10657, 128766, 1555849, 18798954, 227143297, 2744518518, 33161365513, 400680904674, 4841332221601, 58496667563886, 706801342988233, 8540112783422682, 103188154744060417, 1246797969712147686
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n)=12*a(n-1)+a(n-2), n>1 ; a(0)=6, a(1)=73 . G.f.: (6+x)/(1-12*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2008]
a(n)=3*{[6-sqrt(37)]^n+[6+sqrt(37)]^n}+(1/2)*sqrt(37)*{[6+sqrt(37)]^n-[6-sqrt(37)]^n }, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 28 2008]
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MATHEMATICA
| Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[37], n]]], {n, 1, 50}] (*From Vladimir Joseph Stephan Orlovsky, Mar 21 2011*)
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CROSSREFS
| Cf. A041061.
Cf. A089926. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2008]
Sequence in context: A179568 A202557 * A089926 A135594 A168603 A058793
Adjacent sequences: A041057 A041058 A041059 * A041061 A041062 A041063
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KEYWORD
| nonn,cofr,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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