A041260 Numerators of continued fraction convergents to sqrt(142).

11, 12, 131, 143, 3277, 3420, 37477, 40897, 937211, 978108, 10718291, 11696399, 268039069, 279735468, 3065393749, 3345129217, 76658236523, 80003365740, 876691893923, 956695259663, 21923987606509, 22880682866172

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,286,0,0,0,-1).

Formula

a(n) = 286*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 01 2013

G.f.: (11 +12*x +131*x^2 +143*x^3 +131*x^4 -12*x^5 +11*x^6 -x^7) / (1 -286*x^4 +x^8). [Bruno Berselli, Nov 01 2013]

Mathematica

Numerator[Convergents[Sqrt[142], 30]] (* Vincenzo Librandi, Oct 31 2013 *)

Prog

(Magma) I:=[11, 12, 131, 143, 3277, 3420, 37477, 40897]; [n le 8 select I[n] else 286*Self(n-4)-Self(n-8): n in [1..25]]; // Vincenzo Librandi, Nov 01 2013

Crossrefs

Cf. A041261.

Sequence in context: A249312 A357273 A041059 * A109665 A041261 A041262

Adjacent sequences: A041257 A041258 A041259 * A041261 A041262 A041263

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved