A042110 Numerators of continued fraction convergents to sqrt(580).

24, 289, 13896, 167041, 8031864, 96549409, 4642403496, 55805391361, 2683301188824, 32255419657249, 1550943444736776, 18643576756498561, 896442627756667704, 10775955109836511009, 518142287899909196136

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,578,0,-1).

Formula

G.f.: (24 + 289*x + 24*x^2 - x^3)/(1 - 578*x^2 + x^4). - Vincenzo Librandi, Nov 16 2013

a(n) = 578*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 16 2013

Mathematica

Numerator[Convergents[Sqrt[580], 30]] (* or *) CoefficientList[Series[(24 + 289 x + 24 x^2 - x^3)/(1 - 578 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)
LinearRecurrence[{0, 578, 0, -1}, {24, 289, 13896, 167041}, 20] (* Harvey P. Dale, Jun 21 2021 *)

Prog

(Magma) I:=[24, 289, 13896, 167041]; [n le 4 select I[n] else 578*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

Crossrefs

Cf. A042111.

Sequence in context: A035707 A035475 A288458 * A282993 A295272 A369469

Adjacent sequences: A042107 A042108 A042109 * A042111 A042112 A042113

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved