A042705 Denominators of continued fraction convergents to sqrt(882).

1, 1, 3, 10, 63, 199, 461, 660, 38741, 39401, 117543, 392030, 2469723, 7801199, 18072121, 25873320, 1518724681, 1544598001, 4607920683, 15368360050, 96818080983, 305822602999, 708463286981, 1014285889980, 59537044905821, 60551330795801

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,39202,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -x^13 +3*x^12 -10*x^11 +63*x^10 -199*x^9 +461*x^8 -660*x^7 -461*x^6 -199*x^5 -63*x^4 -10*x^3 -3*x^2 -x -1) / ((x^4 -14*x^2 -1)*(x^4 +14*x^2 -1)*(x^8 +198*x^4 +1)). - Colin Barker, Dec 22 2013

a(n) = 39202*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[882], 30]] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 1, 3, 10, 63, 199, 461, 660, 38741, 39401, 117543, 392030, 2469723, 7801199, 18072121, 25873320]; [n le 16 select I[n] else 39202*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A042704, A040852.

Sequence in context: A260969 A305853 A160921 * A041014 A367641 A237998

Adjacent sequences: A042702 A042703 A042704 * A042706 A042707 A042708

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 22 2013

Status

approved