A041982 Numerators of continued fraction convergents to sqrt(514).

22, 23, 68, 1519, 3106, 4625, 206606, 211231, 629068, 14050727, 28730522, 42781249, 1911105478, 1953886727, 5818878932, 129969223231, 265757325394, 395726548625, 17677725464894, 18073452013519

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,9250,0,0,0,0,0,-1).

Formula

G.f.: (22 +23*x +68*x^2 +1519*x^3 +3106*x^4 +4625*x^5 +3106*x^6 -1519*x^7 +68*x^8 -23*x^9 +22*x^10 -x^11)/(1 -9250*x^6 +x^12). - Vincenzo Librandi, Nov 13 2013

a(n) = 9250*a(n-6)-a(n-12). - Vincenzo Librandi, Nov 12 2013

Mathematica

Numerator[Convergents[Sqrt[514], 30]]
(* or *)
CoefficientList[Series[(22 + 23 x + 68 x^2 + 1519 x^3 + 3106 x^4 + 4625 x^5 + 3106 x^6 - 1519 x^7 + 68 x^8 - 23 x^9 + 22 x^10 - x^11)/(1 - 9250 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 13 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 9250, 0, 0, 0, 0, 0, -1}, {22, 23, 68, 1519, 3106, 4625, 206606, 211231, 629068, 14050727, 28730522, 42781249}, 20] (* Harvey P. Dale, Nov 12 2021 *)

Prog

(Magma) I:=[22, 23, 68, 1519, 3106, 4625, 206606, 211231, 629068, 14050727, 28730522, 42781249]; [n le 12 select I[n] else 9250*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 12 2013

Crossrefs

Cf. A041983.

Sequence in context: A041986 A041988 A041984 * A252912 A041992 A041990

Adjacent sequences: A041979 A041980 A041981 * A041983 A041984 A041985

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved