A042582 Numerators of continued fraction convergents to sqrt(820).

28, 29, 57, 86, 229, 315, 3379, 3694, 10767, 14461, 25228, 39689, 2247812, 2287501, 4535313, 6822814, 18180941, 25003755, 268218491, 293222246, 854662983, 1147885229, 2002548212, 3150433441, 178426820908, 181577254349, 360004075257, 541581329606

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,79378,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^23 -28*x^22 +29*x^21 -57*x^20 +86*x^19 -229*x^18 +315*x^17 -3379*x^16 +3694*x^15 -10767*x^14 +14461*x^13 -25228*x^12 -39689*x^11 -25228*x^10 -14461*x^9 -10767*x^8 -3694*x^7 -3379*x^6 -315*x^5 -229*x^4 -86*x^3 -57*x^2 -29*x -28) / ((x^8 -43*x^4 +1)*(x^16 +43*x^12 +1848*x^8 +43*x^4 +1)). - Colin Barker, Dec 18 2013

Mathematica

Numerator[Convergents[Sqrt[820], 30]] (* Vincenzo Librandi, Nov 28 2013 *)

Crossrefs

Cf. A042583, A040791.

Sequence in context: A022398 A042580 A042578 * A042584 A042576 A042574

Adjacent sequences: A042579 A042580 A042581 * A042583 A042584 A042585

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 18 2013

Status

approved