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A041061
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Denominators of continued fraction convergents to sqrt(37).
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6
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1, 12, 145, 1752, 21169, 255780, 3090529, 37342128, 451196065, 5451694908, 65871534961, 795910114440, 9616792908241, 116197425013332, 1403985893068225, 16964028141832032, 204972323595052609, 2476631911282463340, 29924555258984612689, 361571295019097815608
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Sqrt(37) = 6.08276253... = 12/2 + 12/145 + 12/(145*21169) + 12/(21169*3090529) + ... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2008
For positive n, a(n) equals the permanent of the nXn tridiagonal matrix with 12's along the main diagonal and 1's along the superdiagonal and the subdiagonal. [From John M. Campbell, Jul 08 2011]
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..500
Tanya Khovanova, Recursive Sequences
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FORMULA
| 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]
a(n)=((6+sqrt(37))^(n+1)-(6-sqrt(37))^(n+1))/(2*sqrt(37)). [From Rolf Pleisch (r_pleisch(AT)gmx.ch), May 14 2011]
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MATHEMATICA
| 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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PROG
| (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
| Cf. A041060.
Sequence in context: A067219 A075619 A055332 * A174227 A041266 A015501
Adjacent sequences: A041058 A041059 A041060 * A041062 A041063 A041064
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KEYWORD
| nonn,frac,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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