A042406 Numerators of continued fraction convergents to sqrt(731).

27, 730, 39447, 1065799, 57592593, 1556065810, 84085146333, 2271855016801, 122764256053587, 3316906768463650, 179235729753090687, 4842681610101912199, 261684042675256349433, 7070311833842023346890, 382058523070144517081493

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1460,0,-1).

Formula

G.f.: (27 +730*x +27*x^2 -x^3)/(1 -1460*x^2 +x^4). - Vincenzo Librandi, Nov 23 2013

a(n) = 1460*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 23 2013

Mathematica

Numerator[Convergents[Sqrt[731], 30]] (* or *) CoefficientList[Series[(27 + 730 x + 27 x^2 - x^3)/(1 - 1460 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)
LinearRecurrence[{0, 1460, 0, -1}, {27, 730, 39447, 1065799}, 20] (* Harvey P. Dale, Sep 16 2020 *)

Prog

(Magma) I:=[27, 730, 39447, 1065799]; [n le 4 select I[n] else 1460*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 23 2013

Crossrefs

Cf. A042407.

Sequence in context: A009971 A307388 A046240 * A279652 A284039 A159668

Adjacent sequences: A042403 A042404 A042405 * A042407 A042408 A042409

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved