A042693 Denominators of continued fraction convergents to sqrt(876).

1, 1, 2, 5, 72, 149, 221, 370, 21681, 22051, 43732, 109515, 1576942, 3263399, 4840341, 8103740, 474857261, 482961001, 957818262, 2398597525, 34538183612, 71474964749, 106013148361, 177488113110, 10400323708741, 10577811821851, 20978135530592, 52534082883035

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,21902,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -x^13 +2*x^12 -5*x^11 +72*x^10 -149*x^9 +221*x^8 -370*x^7 -221*x^6 -149*x^5 -72*x^4 -5*x^3 -2*x^2 -x -1) / ((x^8 -148*x^4 +1)*(x^8 +148*x^4 +1)). - Colin Barker, Dec 21 2013

a(n) = 21902*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[876], 30]] (* Vincenzo Librandi Dec 21 2013 *)

Prog

(Magma) I:=[1, 1, 2, 5, 72, 149, 221, 370, 21681, 22051, 43732, 109515, 1576942, 3263399, 4840341, 8103740]; [n le 16 select I[n] else 21902*Self(n-8)-Self(n-16): n in [1..70]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A042692, A040846.

Sequence in context: A290864 A309366 A007506 * A328746 A172037 A301993

Adjacent sequences: A042690 A042691 A042692 * A042694 A042695 A042696

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 21 2013

Status

approved