A041090 Numerators of continued fraction convergents to sqrt(53).

7, 22, 29, 51, 182, 2599, 7979, 10578, 18557, 66249, 946043, 2904378, 3850421, 6754799, 24114818, 344362251, 1057201571, 1401563822, 2458765393, 8777860001, 125348805407, 384824276222, 510173081629, 894997357851, 3195165155182, 45627309530399

Offset

0,1

Comments

The terms of this sequence can be constructed with the terms of sequence A086902. For the terms of the periodical sequence of the continued fraction for sqrt(53) see A010139. We observe that its period is five. The decimal expansion of sqrt(53) is A010506. - Johannes W. Meijer, Jun 12 2010

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,364,0,0,0,0,1).

Formula

a(5*n) = A086902(3*n+1), a(5*n+1) = (A086902(3*n+2)-A086902(3*n+1))/2, a(5*n+2) = (A086902(3*n+2)+A086902(3*n+1))/2, a(5*n+3) = A086902(3*n+2) and a(5*n+4) = A086902(3*n+3)/2. - Johannes W. Meijer, Jun 12 2010

G.f.: -(x^9-7*x^8+22*x^7-29*x^6+51*x^5+182*x^4+51*x^3+29*x^2+22*x+7) / (x^10+364*x^5-1). - Colin Barker, Sep 26 2013

Mathematica

Numerator[Convergents[Sqrt[53], 30]] (* Harvey P. Dale, Sep 24 2013 *)
CoefficientList[Series[-(x^9 - 7 x^8 + 22 x^7 - 29 x^6 + 51 x^5 + 182 x^4 + 51 x^3 + 29 x^2 + 22 x + 7)/(x^10 + 364 x^5 - 1), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 27 2013 *)

Crossrefs

Cf. A041091, A041018, A041046, A041150, A041226, A041318, A041426 and A041550.

Sequence in context: A286572 A055575 A297712 * A042639 A287166 A229978

Adjacent sequences: A041087 A041088 A041089 * A041091 A041092 A041093

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Sep 26 2013

Status

approved