A042626 Numerators of continued fraction convergents to sqrt(843).

29, 842, 48865, 1417927, 82288631, 2387788226, 138574005739, 4021033954657, 233358543375845, 6771418791854162, 392975648470917241, 11403065224448454151, 661770758666481257999, 19202755066552404936122

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, 1684, 0, -1).

Formula

G.f.: (29 +842*x +29*x^2 -x^3)/(1 -1684*x^2 +x^4). - Vincenzo Librandi, Nov 30 2013

a(n) = 1684*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 30 2013

Mathematica

Numerator[Convergents[Sqrt[843], 30]] (* or *) CoefficientList[Series[(29 + 842 x + 29 x^2 - x^3)/(1 - 1684 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 30 2013 *)

Prog

(Magma) I:=[29, 842, 48865, 1417927]; [n le 4 select I[n] else 1684*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 30 2013

Crossrefs

Cf. A042627.

Sequence in context: A278475 A057687 A049667 * A157877 A158665 A324432

Adjacent sequences: A042623 A042624 A042625 * A042627 A042628 A042629

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved