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A042012 Numerators of continued fraction convergents to sqrt(530). 2
23, 1059, 48737, 2242961, 103224943, 4750590339, 218630380537, 10061748095041, 463059042752423, 21310777714706499, 980758833919251377, 45136217138000269841, 2077246747181931664063, 95598486587506856816739, 4399607629772497345234057 (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 (46,1).

FORMULA

a(n)=46*a(n-1)+a(n-2), n>1 ; a(0)=23, a(1)=1059 . G.f.: (23+x)/(1-46*x-x^2). [From Philippe Deléham, Nov 23 2008]

a(n)=(1/2)*sqrt(530)*{[23+sqrt(530)]^n-[23-sqrt(530)]^n}+(23/2)*{[23+sqrt(530)]^n+[23-sqrt(530)]^n}, with n>=0 [From Paolo P. Lava, Nov 28 2008]

MATHEMATICA

Numerator[Convergents[Sqrt[530], 30]] (* Vincenzo Librandi, Nov 13 2013 *)

LinearRecurrence[{46, 1}, {23, 1059}, 30] (* Harvey P. Dale, May 05 2016 *)

CROSSREFS

Cf. A042013, A040506.

Sequence in context: A069479 A174748 A042015 * A128404 A126741 A273477

Adjacent sequences:  A042009 A042010 A042011 * A042013 A042014 A042015

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Additional term from Colin Barker, Nov 29 2013

STATUS

approved

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Last modified August 21 09:54 EDT 2017. Contains 290864 sequences.