A041722 Numerators of continued fraction convergents to sqrt(381).

19, 20, 39, 488, 527, 1015, 39097, 40112, 79209, 990620, 1069829, 2060449, 79366891, 81427340, 160794231, 2010958112, 2171752343, 4182710455, 161114749633, 165297460088, 326412209721, 4082243976740, 4408656186461, 8490900163201, 327062862388099

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, 2030, 0, 0, 0, 0, 0, -1).

Formula

a(n) = 2030*a(n-6) - a(n-12) for n>11. [Bruno Berselli, Nov 07 2013]

G.f.: -(x^11 -19*x^10 +20*x^9 -39*x^8 +488*x^7 -527*x^6 -1015*x^5 -527*x^4 -488*x^3 -39*x^2 -20*x -19) / (x^12 -2030*x^6 +1). - Colin Barker, Dec 28 2013

Mathematica

Numerator[Convergents[Sqrt[381], 30]] (* Harvey P. Dale, Mar 26 2013 *)

Prog

(Magma) I:=[19, 20, 39, 488, 527, 1015, 39097, 40112, 79209, 990620, 1069829, 2060449]; [n le 12 select I[n] else 2030*Self(n-6)-Self(n-12): n in [1..30]]; // Bruno Berselli, Nov 07 2013

Crossrefs

Cf. A041723, A040361.

Sequence in context: A041728 A041726 A041724 * A041738 A041740 A041736

Adjacent sequences: A041719 A041720 A041721 * A041723 A041724 A041725

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 28 2013

Status

approved