A041809 Denominators of continued fraction convergents to sqrt(425).

1, 1, 2, 3, 5, 8, 13, 528, 541, 1069, 1610, 2679, 4289, 6968, 283009, 289977, 572986, 862963, 1435949, 2298912, 3734861, 151693352, 155428213, 307121565, 462549778, 769671343, 1232221121, 2001892464, 81307919681, 83309812145, 164617731826, 247927543971

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, 536, 0, 0, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^12-x^11+2*x^10-3*x^9+5*x^8-8*x^7+13*x^6+8*x^5+5*x^4+3*x^3+2*x^2+x+1) / (x^14+536*x^7-1). - Colin Barker, Nov 25 2013

a(n) = 536*a(n-7) + a(n-14) for n>13. - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[425], 30]] (* Vincenzo Librandi, Dec 24 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 536, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 2, 3, 5, 8, 13, 528, 541, 1069, 1610, 2679, 4289, 6968}, 40] (* Harvey P. Dale, Dec 02 2014 *)

Prog

(Magma) I:=[1, 1, 2, 3, 5, 8, 13, 528, 541, 1069, 1610, 2679, 4289, 6968]; [n le 14 select I[n] else 536*Self(n-7)+Self(n-14): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041808, A040404.

Sequence in context: A294939 A096095 A041101 * A117566 A123000 A132599

Adjacent sequences: A041806 A041807 A041808 * A041810 A041811 A041812

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 25 2013

Status

approved