A041968 Numerators of continued fraction convergents to sqrt(507).

22, 23, 45, 653, 698, 1351, 60142, 61493, 121635, 1764383, 1886018, 3650401, 162503662, 166154063, 328657725, 4767362213, 5096019938, 9863382151, 439084834582, 448948216733, 888033051315, 12881410935143, 13769443986458, 26650854921601, 1186407060536902

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, 2702, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^11 -22*x^10 +23*x^9 -45*x^8 +653*x^7 -698*x^6 -1351*x^5 -698*x^4 -653*x^3 -45*x^2 -23*x -22) / ((x^2 -4*x +1)*(x^2 +4*x +1)*(x^4 -4*x^3 +15*x^2 -4*x +1)*(x^4 +4*x^3 +15*x^2 +4*x +1)). - Colin Barker, Nov 28 2013

Mathematica

Numerator[Convergents[Sqrt[507], 30]] (* Vincenzo Librandi, Nov 12 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 2702, 0, 0, 0, 0, 0, -1}, {22, 23, 45, 653, 698, 1351, 60142, 61493, 121635, 1764383, 1886018, 3650401}, 30] (* Harvey P. Dale, Nov 15 2023 *)

Crossrefs

Cf. A041969, A040484.

Sequence in context: A041974 A041972 A041970 * A041986 A041988 A041984

Adjacent sequences: A041965 A041966 A041967 * A041969 A041970 A041971

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved