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A041318
Numerators of continued fraction convergents to sqrt(173).
10
13, 79, 92, 171, 1118, 29239, 176552, 205791, 382343, 2499849, 65378417, 394770351, 460148768, 854919119, 5589663482, 146186169651, 882706681388, 1028892851039, 1911599532427, 12498490045601, 326872340718053, 1973732534353919, 2300604875071972
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 2236, 0, 0, 0, 0, 1).
FORMULA
a(5*n) = A088316(3*n+1), a(5*n+1) = (A088316(3*n+2) - A088316(3*n+1))/2, a(5*n+2) = (A088316(3*n+2)+A088316(3*n+1))/2, a(5*n+3) = A088316(3*n+2) and a(5*n+4) = A088316(3*n+3)/2. [Johannes W. Meijer, Jun 12 2010]
G.f.: -(x^9-13*x^8+79*x^7-92*x^6+171*x^5+1118*x^4+171*x^3+92*x^2+79*x+13) / (x^10+2236*x^5-1). - Colin Barker, Nov 08 2013
MATHEMATICA
Numerator[Convergents[Sqrt[173], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0, 0, 0, 0, 2236, 0, 0, 0, 0, 1}, {13, 79, 92, 171, 1118, 29239, 176552, 205791, 382343, 2499849}, 30] (* Harvey P. Dale, Jul 28 2018 *)
CROSSREFS
Cf. A010217 (continued fraction).
Sequence in context: A022608 A060216 A374425 * A142056 A173831 A081584
KEYWORD
nonn,frac,cofr,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 08 2013
STATUS
approved