A042131 Denominators of continued fraction convergents to sqrt(590).

1, 3, 7, 31, 69, 238, 11493, 34717, 80927, 358425, 797777, 2751756, 132882065, 401397951, 935677967, 4144109819, 9223897605, 31815802634, 1536382424037, 4640963074745, 10818308573527, 47914197368853, 106646703311233, 367854307302552, 17763653453833729

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,11562,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-3*x^9+7*x^8-31*x^7+69*x^6-238*x^5-69*x^4-31*x^3-7*x^2-3*x-1) / (x^12-11562*x^6+1). - Colin Barker, Dec 02 2013

a(n) = 11562*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[590], 30]] (* Vincenzo Librandi, Jan 15 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 11562, 0, 0, 0, 0, 0, -1}, {1, 3, 7, 31, 69, 238, 11493, 34717, 80927, 358425, 797777, 2751756}, 30] (* Harvey P. Dale, May 15 2022 *)

Crossrefs

Cf. A042130, A040565.

Sequence in context: A080168 A183075 A292890 * A109140 A088193 A091383

Adjacent sequences: A042128 A042129 A042130 * A042132 A042133 A042134

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved