A041676 Numerators of continued fraction convergents to sqrt(357).

18, 19, 170, 359, 3042, 3401, 125478, 128879, 1156510, 2441899, 20691702, 23133601, 853501338, 876634939, 7866580850, 16609796639, 140744953962, 157354750601, 5805515975598, 5962870726199, 53508481785190, 112979834296579, 957347156157822

Offset

0,1

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, 6802, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^11-18*x^10+19*x^9-170*x^8+359*x^7-3042*x^6-3401*x^5-3042*x^4-359*x^3-170*x^2-19*x-18)/(x^12-6802*x^6+1). - Vincenzo Librandi, Nov 06 2013

a(n) = 6802*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 06 2013

Mathematica

Numerator[Convergents[Sqrt[357], 30]] (* Harvey P. Dale, Mar 06 2012 *)
CoefficientList[Series[-(x^11 - 18 x^10 + 19 x^9 - 170 x^8 + 359 x^7 - 3042 x^6 - 3401 x^5 - 3042 x^4 - 359 x^3 - 170 x^2 - 19 x - 18)/(x^12 - 6802 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 06 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 6802, 0, 0, 0, 0, 0, -1}, {18, 19, 170, 359, 3042, 3401, 125478, 128879, 1156510, 2441899, 20691702, 23133601}, 30] (* Bruno Berselli, Nov 06 2013 *)

Prog

(Magma) I:=[18, 19, 170, 359, 3042, 3401, 125478, 128879, 1156510, 2441899, 20691702, 23133601]; [n le 12 select I[n] else 6802*Self(n-6)-Self(n-12): n in [1..25]]; // Vincenzo Librandi, Nov 06 2013

Crossrefs

Cf. A041677.

Sequence in context: A041670 A041672 A041674 * A370152 A041678 A197352

Adjacent sequences: A041673 A041674 A041675 * A041677 A041678 A041679

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved