A042432 Numerators of continued fraction convergents to sqrt(744).

27, 82, 109, 191, 300, 491, 791, 1282, 2073, 7501, 407127, 1228882, 1636009, 2864891, 4500900, 7365791, 11866691, 19232482, 31099173, 112530001, 6107719227, 18435687682, 24543406909, 42979094591, 67522501500, 110501596091, 178024097591, 288525693682

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,15002,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^19 -27*x^18 +82*x^17 -109*x^16 +191*x^15 -300*x^14 +491*x^13 -791*x^12 +1282*x^11 -2073*x^10 -7501*x^9 -2073*x^8 -1282*x^7 -791*x^6 -491*x^5 -300*x^4 -191*x^3 -109*x^2 -82*x -27) / (x^20 -15002*x^10 +1). - Colin Barker, Dec 14 2013

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[744], n]]], {n, 1, 50}] (* Artur Jasinski, Dec 20 2008 *)
Numerator[Convergents[Sqrt[744], 30]] (* Vincenzo Librandi, Nov 24 2013 *)

Crossrefs

Cf. A042433, A040716.

Sequence in context: A008884 A031455 A045004 * A042430 A195028 A042434

Adjacent sequences: A042429 A042430 A042431 * A042433 A042434 A042435

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 14 2013

Status

approved