A041014 Numerators of continued fraction convergents to sqrt(11).

3, 10, 63, 199, 1257, 3970, 25077, 79201, 500283, 1580050, 9980583, 31521799, 199111377, 628855930, 3972246957, 12545596801, 79245827763, 250283080090, 1580944308303, 4993116004999, 31539640338297

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,20,0,-1).

Formula

G.f.: (3 + 10*x + 3*x^2 - x^3)/(1 - 20*x^2 + x^4).

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[11], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011 *)
Numerator[Convergents[Sqrt[11], 30]] (* Vincenzo Librandi, Oct 28 2013 *)

Prog

(PARI) A041014=contfracpnqn(c=contfrac(sqrt(11)), #c)[1, ][^-1] \\ Discard last element which may be incorrect. Use e.g. \p999 to get more terms, or extend as follows:
{A041014_upto(N, A=Vec(A041014, N))=for(n=#A041014+1, N, A[n]=20*A[n-2]-A[n-4]); A041014=A} \\ M. F. Hasler, Nov 01 2019

Crossrefs

Cf. A010468, A041015 (denominators).

Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041008 (m=7), A041010 (m=8), A005667 (m=10), A041016 (m=12), ..., A042936 (m=1000).

Sequence in context: A305853 A160921 A042705 * A367641 A237998 A167939

Adjacent sequences: A041011 A041012 A041013 * A041015 A041016 A041017

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved