A042297 Denominators of continued fraction convergents to sqrt(674).

1, 1, 25, 26, 1325, 1351, 33749, 35100, 1788749, 1823849, 45561125, 47384974, 2414809825, 2462194799, 61507485001, 63969679800, 3259991475001, 3323961154801, 83035059190225, 86359020345026, 4400986076441525, 4487345096786551, 112097268399318749

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1350,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+26*x^2+1) / (x^8-1350*x^4+1). - Colin Barker, Dec 07 2013

a(n) = 1350*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Jan 19 2014

Mathematica

Denominator[Convergents[Sqrt[674], 30]] (* Vincenzo Librandi, Jan 19 2014 *)

Prog

(Magma) I:=[1, 1, 25, 26, 1325, 1351, 33749, 35100]; [n le 8 select I[n] else 1350*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Jan 19 2014

Crossrefs

Cf. A042296, A040648.

Sequence in context: A042294 A041311 A042296 * A042298 A157091 A070662

Adjacent sequences: A042294 A042295 A042296 * A042298 A042299 A042300

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 07 2013

Status

approved