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Search: id:A041112
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| A041112 |
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Numerators of continued fraction convergents to sqrt(65). |
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+0
2
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| 8, 129, 2072, 33281, 534568, 8586369, 137916472, 2215249921, 35581915208, 571525893249, 9179996207192, 147451465208321, 2368403439540328, 38041906497853569, 611038907405197432, 9814664424981012481
(list; graph; listen)
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OFFSET
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0,1
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)=16*a(n-1)+a(n-2), n>1 ; a(0)=8, a(1)=129 . G.f.: (8+x)/(1-16*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2008]
a(n)=(1/2)*sqrt(65)*{[8+sqrt(65)]^n-[8-sqrt(65)]^n}+4*{[8-sqrt(65)]^n+[8+sqrt(65)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 28 2008]
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CROSSREFS
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Cf. A041113.
Sequence in context: A104997 A027951 A041115 this_sequence A073701 A079912 A128287
Adjacent sequences: A041109 A041110 A041111 this_sequence A041113 A041114 A041115
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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