A041745 Denominators of continued fraction convergents to sqrt(392).

1, 1, 4, 5, 194, 199, 791, 990, 38411, 39401, 156614, 196015, 7605184, 7801199, 31008781, 38809980, 1505788021, 1544598001, 6139582024, 7684180025, 298138422974, 305822602999, 1215606231971, 1521428834970, 59029901960831, 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 (0,0,0,198,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+5*x^2+1) / ((x^4-14*x^2-1)*(x^4+14*x^2-1)). - Colin Barker, Nov 23 2013

a(n) = 198*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[392], 30]] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(Magma) I:=[1, 1, 4, 5, 194, 199, 791, 990]; [n le 8 select I[n] else 198*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041744, A040372.

Sequence in context: A101076 A331578 A355705 * A298224 A051152 A042181

Adjacent sequences: A041742 A041743 A041744 * A041746 A041747 A041748

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 23 2013

Status

approved