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A041264
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Numerators of continued fraction convergents to sqrt(145).
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1
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12, 289, 6948, 167041, 4015932, 96549409, 2321201748, 55805391361, 1341650594412, 32255419657249, 775471722368388, 18643576756498561, 448221313878333852, 10775955109836511009, 259071143949954598068
(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)=24*a(n-1)+a(n-2), n>1 ; a(0)=12, a(1)=289 . G.f.: (12+x)/(1-24*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2008]
a(n)=6*{[12+sqrt(145)]^n+[12-sqrt(145)]^n}+(1/2)*sqrt(145)*{[12+sqrt(145)]^n - [12-sqrt(145)]^n}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 28 2008]
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CROSSREFS
| Cf. A041265.
Sequence in context: A145448 A001164 A041267 * A109867 A014130 A054942
Adjacent sequences: A041261 A041262 A041263 * A041265 A041266 A041267
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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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EXTENSIONS
| Corrected second formula. - Paolo P. Lava (paoloplava(AT)gmail.com), Dec 01 2008
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