A041226 Numerators of continued fraction convergents to sqrt(125).

11, 56, 67, 123, 682, 15127, 76317, 91444, 167761, 930249, 20633239, 104096444, 124729683, 228826127, 1268860318, 28143753123, 141987625933, 170131379056, 312119004989, 1730726404001, 38388099893011, 193671225869056, 232059325762067, 425730551631123

Offset

0,1

Comments

From Johannes W. Meijer, Jun 12 2010: (Start)

The a(n) terms of this sequence can be constructed with the terms of sequence A001946.

For the terms of the periodical sequence of the continued fraction for sqrt(125) see A010186. We observe that its period is five. (End)

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1364,0,0,0,0,1).

Formula

From Johannes W. Meijer, Jun 12 2010: (Start)

a(5n) = A001946(3n+1),

a(5n+1) = (A001946(3n+2) - A001946(3n+1))/2,

a(5n+2) = (A001946(3n+2) + A001946(3n+1))/2,

a(5n+3) = A001946(3n+2),

a(5n+4) = A001946(3n+3)/2. (End)

G.f.: -(x^9 -11*x^8 +56*x^7 -67*x^6 +123*x^5 +682*x^4 +123*x^3 +67*x^2 +56*x +11) / ((x^2 +4*x -1)*(x^4 -7*x^3 +19*x^2 -3*x +1)*(x^4 +3*x^3 +19*x^2 +7*x +1)). - Colin Barker, Nov 08 2013

Mathematica

Numerator[Convergents[Sqrt[125], 30]] (* Vincenzo Librandi, Oct 31 2013 *)

Crossrefs

Cf. A041227, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550.

Sequence in context: A206528 A259193 A099532 * A042503 A223766 A265151

Adjacent sequences: A041223 A041224 A041225 * A041227 A041228 A041229

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 08 2013

Status

approved