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Search: id:A041061
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| A041061 |
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Denominators of continued fraction convergents to sqrt(37). |
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+0
4
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| 1, 12, 145, 1752, 21169, 255780, 3090529, 37342128, 451196065, 5451694908, 65871534961, 795910114440, 9616792908241, 116197425013332, 1403985893068225, 16964028141832032, 204972323595052609
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sqrt(37) = 6.08276253... = 12/2 + 12/145 + 12/(145*21169) + 12/(21169*3090529) + ... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2008
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)=F(n, 12), the n-th Fibonacci polynomial evaluated at x=12. - T. D. Noe (noe(AT)sspectra.com), Jan 19 2006
a(n)=12*a(n-1)+a(n-2), n>1 ; a(0)=1, a(1)=12. G.f.: 1/(1-12*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2008]
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MATHEMATICA
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a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*12, {n, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 27 2009]
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PROGRAM
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(Other) sage: [lucas_number1(n, 12, -1) for n in xrange(1, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 28 2009]
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CROSSREFS
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Cf. A041060.
Sequence in context: A067219 A075619 A055332 this_sequence A041266 A015501 A039493
Adjacent sequences: A041058 A041059 A041060 this_sequence A041062 A041063 A041064
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KEYWORD
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nonn,frac,easy,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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