A041074 Numerators of continued fraction convergents to sqrt(44).

6, 7, 13, 20, 53, 73, 126, 199, 2514, 2713, 5227, 7940, 21107, 29047, 50154, 79201, 1000566, 1079767, 2080333, 3160100, 8400533, 11560633, 19961166, 31521799, 398222754, 429744553, 827967307, 1257711860

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,398,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^15 -6*x^14 +7*x^13 -13*x^12 +20*x^11 -53*x^10 +73*x^9 -126*x^8 -199*x^7 -126*x^6 -73*x^5 -53*x^4 -20*x^3 -13*x^2 -7*x -6) / ((x^8 -20*x^4 +1)*(x^8 +20*x^4 +1)). - Colin Barker, Nov 04 2013

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[44], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*)
Numerator[Convergents[Sqrt[44], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Crossrefs

Cf. A041075, A010498.

Sequence in context: A070398 A022096 A041175 * A041749 A042723 A160825

Adjacent sequences: A041071 A041072 A041073 * A041075 A041076 A041077

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved