A042640 Numerators of continued fraction convergents to sqrt(850).

29, 175, 379, 2449, 142421, 856975, 1856371, 11995201, 697578029, 4197463375, 9092504779, 58752492049, 3416737043621, 20559174753775, 44535086551171, 287769694060801, 16735177342077629, 100698833746526575

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, 4898, 0, 0, 0, -1).

Formula

G.f.: (29 +175*x +379*x^2 +2449*x^3 +379*x^4 -175*x^5 +29*x^6 -x^7)/(1 -4898*x^4 +x^8). - Vincenzo Librandi, Nov 30 2013

a(n) = 4898*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 30 2013

Mathematica

Numerator[Convergents[Sqrt[850], 30]] (* Harvey P. Dale, Oct 27 2011 *)
CoefficientList[Series[(29 + 175 x + 379 x^2 + 2449 x^3 + 379 x^4 - 175 x^5 + 29 x^6 - x^7)/(1 - 4898 x^4 + x^8), {x, 0, 30}], x]  (* Vincenzo Librandi, Nov 30 2013 *)

Prog

(Magma) I:=[29, 175, 379, 2449, 142421, 856975, 1856371, 11995201]; [n le 8 select I[n] else 4898*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 30 2013

Crossrefs

Cf. A042641.

Sequence in context: A033219 A142407 A183714 * A140573 A165613 A302450

Adjacent sequences: A042637 A042638 A042639 * A042641 A042642 A042643

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved