A041038 Numerators of continued fraction convergents to sqrt(24).

4, 5, 44, 49, 436, 485, 4316, 4801, 42724, 47525, 422924, 470449, 4186516, 4656965, 41442236, 46099201, 410235844, 456335045, 4060916204, 4517251249, 40198926196, 44716177445, 397928345756

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,10,0,-1).

Formula

a(2n) = 2*A041006(2n) ; a(2n-1) = A041006(2n-1) = A001079(n). [From M. F. Hasler, Feb 13 2009]

G.f.: (4+5*x+4*x^2-x^3)/(1-10*x^2+x^4)

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[24], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011*)
Numerator[Convergents[Sqrt[24], 30]] (* Vincenzo Librandi, Oct 28 2013 *)

Crossrefs

Cf. A010480, A041039.

Sequence in context: A271293 A256290 A041037 * A239860 A151486 A042383

Adjacent sequences: A041035 A041036 A041037 * A041039 A041040 A041041

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved