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A041264 Numerators of continued fraction convergents to sqrt(145). 2
12, 289, 6948, 167041, 4015932, 96549409, 2321201748, 55805391361, 1341650594412, 32255419657249, 775471722368388, 18643576756498561, 448221313878333852, 10775955109836511009, 259071143949954598068, 6228483409908746864641, 149742672981759879349452 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (24,1).

FORMULA

a(n) = 24*a(n-1)+a(n-2) for n>1; a(0)=12, a(1)=289. G.f.: (12+x)/(1-24*x-x^2). [Philippe Deléham, 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). [Paolo P. Lava, Nov 28 2008]

MATHEMATICA

Numerator[Convergents[Sqrt[145], 30]] (* Vincenzo Librandi, Oct 31 2013 *)

CROSSREFS

Cf. A041265.

Sequence in context: A001164 A226100 A041267 * A220307 A223011 A245915

Adjacent sequences:  A041261 A041262 A041263 * A041265 A041266 A041267

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected second formula. - Paolo P. Lava, Dec 01 2008

More terms from Colin Barker, Nov 06 2013

STATUS

approved

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Last modified June 27 19:44 EDT 2017. Contains 288790 sequences.