A042815 Denominators of continued fraction convergents to sqrt(938).

1, 1, 2, 3, 8, 67, 142, 209, 351, 560, 33951, 34511, 68462, 102973, 274408, 2298237, 4870882, 7169119, 12040001, 19209120, 1164587201, 1183796321, 2348383522, 3532179843, 9412743208, 78834125507, 167080994222

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, 0, 0, 34302, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +8*x^14 -67*x^13 +142*x^12 -209*x^11 +351*x^10 -560*x^9 -351*x^8 -209*x^7 -142*x^6 -67*x^5 -8*x^4 -3*x^3 -2*x^2 -x -1) / (x^20 -34302*x^10 +1). - Colin Barker, Dec 24 2013

a(n) = 34302*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Jan 30 2014

Mathematica

Denominator[Convergents[Sqrt[938], 50]] (* Harvey P. Dale, Sep 16 2011 *)

Prog

(Magma) I:=[1, 1, 2, 3, 8, 67, 142, 209, 351, 560, 33951, 34511, 68462, 102973, 274408, 2298237, 4870882, 7169119, 12040001, 19209120]; [n le 20 select I[n] else 34302*Self(n-10)-Self(n-20): n in [1..30]]; // Vincenzo Librandi, Jan 30 2014

Crossrefs

Cf. A042814, A040907.

Sequence in context: A003096 A333077 A354574 * A191353 A319218 A358562

Adjacent sequences: A042812 A042813 A042814 * A042816 A042817 A042818

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Dec 24 2013

Status

approved