A042863 Denominators of continued fraction convergents to sqrt(963).

1, 31, 1923, 59644, 3699851, 114755025, 7118511401, 220788608456, 13696012235673, 424797167914319, 26351120422923451, 817309530278541300, 50699541997692484051, 1572503111458745546881, 97545892452439916390673, 3025495169137096153657744

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, 1924, 0, -1).

Formula

G.f.: -(x^2 - 31*x - 1) / (x^4 - 1924*x^2 + 1). - Colin Barker, Dec 25 2013

a(n) = 1924*a(n-2) - a(n-4) for n > 3. - Vincenzo Librandi, Dec 25 2013

Mathematica

Denominator[Convergents[Sqrt[963], 30]] (* Vincenzo Librandi, Dec 25 2013 *)
LinearRecurrence[{0, 1924, 0, -1}, {1, 31, 1923, 59644}, 20] (* Harvey P. Dale, Oct 28 2025 *)

Prog

(Magma) I:=[1, 31, 1923, 59644]; [n le 4 select I[n] else 1924*Self(n-2)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Dec 25 2013

Crossrefs

Cf. A042862, A040931.

Sequence in context: A338533 A055629 A131751 * A042860 A184488 A218352

Adjacent sequences: A042860 A042861 A042862 * A042864 A042865 A042866

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

Additional term from Colin Barker, Dec 25 2013

Status

approved