A042811 Denominators of continued fraction convergents to sqrt(936).

1, 1, 2, 5, 32, 69, 101, 170, 10301, 10471, 20772, 52015, 332862, 717739, 1050601, 1768340, 107151001, 108919341, 216070342, 541060025, 3462430492, 7465921009, 10928351501, 18394272510, 1114584702101, 1132978974611, 2247563676712, 5628106328035

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, 10402, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -x^13 +2*x^12 -5*x^11 +32*x^10 -69*x^9 +101*x^8 -170*x^7 -101*x^6 -69*x^5 -32*x^4 -5*x^3 -2*x^2 -x -1) / ((x^4 -10*x^2 -1)*(x^4 +10*x^2 -1)*(x^8 +102*x^4 +1)). - Colin Barker, Dec 23 2013

a(n) = 10402*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Jan 30 2014

Mathematica

Denominator/@Convergents[Sqrt[936], 30]  (* Harvey P. Dale, Apr 18 2011 *)

Prog

(Magma) I:=[1, 1, 2, 5, 32, 69, 101, 170, 10301, 10471, 20772, 52015, 332862, 717739, 1050601, 1768340]; [n le 16 select I[n] else 10402*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Jan 30 2014

Crossrefs

Cf. A042810, A040905.

Sequence in context: A364270 A032504 A041397 * A261045 A145656 A221680

Adjacent sequences: A042808 A042809 A042810 * A042812 A042813 A042814

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 23 2013

Status

approved