A042681 Denominators of continued fraction convergents to sqrt(870).

1, 2, 117, 236, 13805, 27846, 1628873, 3285592, 192193209, 387672010, 22677169789, 45742011588, 2675713841893, 5397169695374, 315711556173585, 636820282042544, 37251287914641137, 75139396111324818, 4395336262371480581, 8865811920854285980

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,118,0,-1).

Formula

G.f.: -(x^2-2*x-1) / (x^4-118*x^2+1). - Colin Barker, Dec 21 2013

a(n) = 118*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[870], 30]] (* Vincenzo Librandi Dec 21 2013 *)
LinearRecurrence[{0, 118, 0, -1}, {1, 2, 117, 236}, 20] (* Harvey P. Dale, Jul 16 2018 *)

Prog

(Magma) I:=[1, 2, 117, 236]; [n le 4 select I[n] else 118*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A042680, A040840.

Sequence in context: A257939 A203607 A188977 * A024243 A307094 A147774

Adjacent sequences: A042678 A042679 A042680 * A042682 A042683 A042684

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Dec 21 2013

Status

approved