A042660 Numerators of continued fraction convergents to sqrt(860).

29, 88, 1261, 3871, 225779, 681208, 9762691, 29969281, 1747980989, 5273912248, 75582752461, 232022169631, 13532868591059, 40830627942808, 585161659790371, 1796315607313921, 104771466883997789, 316110716259307288

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,7742,0,0,0,-1).

Formula

G.f.: (29 +88*x +1261*x^2 +3871*x^3 +1261*x^4 -88*x^5 +29*x^6 -x^7)/(1 -7742*x^4 +x^8). - Vincenzo Librandi, Nov 30 2013

a(n) = 7742*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 30 2013

Mathematica

Numerator[Convergents[Sqrt[860], 30]] (* Harvey P. Dale, Mar 04 2013 *)
CoefficientList[Series[(29 + 88 x + 1261 x^2 + 3871 x^3 + 1261 x^4 - 88 x^5 + 29 x^6 - x^7)/(1 - 7742 x^4 + x^8), {x, 0, 30}], x]  (* Vincenzo Librandi, Nov 30 2013 *)

Prog

(Magma) I:=[29, 88, 1261, 3871, 225779, 681208, 9762691, 29969281]; [n le 8 select I[n] else 7742*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 30 2013

Crossrefs

Cf. A042661.

Sequence in context: A042652 A042656 A042658 * A047650 A308787 A141883

Adjacent sequences: A042657 A042658 A042659 * A042661 A042662 A042663

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved