A042408 Numerators of continued fraction convergents to sqrt(732).

27, 487, 26325, 474337, 25640523, 462003751, 24973843077, 449991179137, 24324497516475, 438290946475687, 23692035607203573, 426894931876140001, 23076018356918763627, 415795225356413885287, 22476018187603268569125

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, 974, 0, -1).

Formula

G.f.: (27 +487*x +27*x^2 -x^3)/(1 -974*x^2 +x^4). - Vincenzo Librandi, Nov 23 2013

a(n) = 974*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 23 2013

Mathematica

Numerator[Convergents[Sqrt[732], 30]] (* or *) CoefficientList[Series[(27 + 487 x + 27 x^2 - x^3)/(1 - 974 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)
LinearRecurrence[{0, 974, 0, -1}, {27, 487, 26325, 474337}, 20] (* Harvey P. Dale, May 07 2015 *)

Prog

(Magma) I:=[27, 487, 26325, 474337]; [n le 4 select I[n] else 974*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 23 2013

Crossrefs

Cf. A042409.

Sequence in context: A020976 A024114 A025982 * A023946 A020971 A023772

Adjacent sequences: A042405 A042406 A042407 * A042409 A042410 A042411

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved