A041212 Numerators of continued fraction convergents to sqrt(117).

10, 11, 54, 119, 530, 649, 13510, 14159, 70146, 154451, 687950, 842401, 17535970, 18378371, 91049454, 200477279, 892958570, 1093435849, 22761675550, 23855111399, 118182121146, 260219353691, 1159059535910

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1298,0,0,0,0,0,-1).

Formula

From Colin Barker, Jul 19 2012: (Start)

a(n) = 1298*a(n-6) - a(n-12).

G.f.: -(x^11 - 10*x^10 + 11*x^9 - 54*x^8 + 119*x^7 - 530*x^6 - 649*x^5 - 530*x^4 - 119*x^3 - 54*x^2 - 11*x - 10)/((x^2 - 3*x - 1)*(x^2 + 3*x - 1)*(x^4 - 3*x^3 + 10*x^2 + 3*x + 1)*(x^4 + 3*x^3 + 10*x^2 - 3*x + 1)). (End)

Mathematica

Numerator[Convergents[Sqrt[117], 30]] (* Vincenzo Librandi, Oct 26 2013 *)

Crossrefs

Cf. A010182, A041213.

Sequence in context: A267340 A344082 A042413 * A257313 A335553 A122602

Adjacent sequences: A041209 A041210 A041211 * A041213 A041214 A041215

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved