A042266 Numerators of continued fraction convergents to sqrt(659).

25, 26, 77, 1951, 3979, 5930, 300479, 306409, 913297, 23138834, 47190965, 70329799, 3563680915, 3634010714, 10831702343, 274426569289, 559684840921, 834111410210, 42265255351421, 43099366761631

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 11860, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (25 + 26*x + 77*x^2 + 1951*x^3 + 3979*x^4 + 5930*x^5 + 3979*x^6 - 1951*x^7 + 77*x^8 - 26*x^9 + 25*x^10 - x^11)/(1 - 11860*x^6 + x^12). - Vincenzo Librandi, Nov 20 2013

a(n) = 11860*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 18 2013

Mathematica

Numerator[Convergents[Sqrt[659], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 77 x^2 + 1951 x^3 + 3979 x^4 + 5930 x^5 + 3979 x^6 - 1951 x^7 + 77 x^8 - 26 x^9 + 25 x^10 - x^11)/(1 - 11860 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 20 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 11860, 0, 0, 0, 0, 0, -1}, {25, 26, 77, 1951, 3979, 5930, 300479, 306409, 913297, 23138834, 47190965, 70329799}, 30] (* Harvey P. Dale, Jan 04 2023 *)

Prog

(Magma) I:=[25, 26, 77, 1951, 3979, 5930, 300479, 306409, 913297, 23138834, 47190965, 70329799]; [n le 12 select I[n] else 11860*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Crossrefs

Cf. A042267.

Sequence in context: A042274 A042270 A042268 * A042278 A042276 A042282

Adjacent sequences: A042263 A042264 A042265 * A042267 A042268 A042269

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved