A042117 Denominators of continued fraction convergents to sqrt(583).

1, 6, 7, 55, 282, 1183, 6197, 44562, 50759, 349116, 16808327, 101199078, 118007405, 927250913, 4754261970, 19944298793, 104475755935, 751274590338, 855750346273, 5885776667976, 283373030409121, 1706123959122702, 1989496989531823, 15632602885845463

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, 0, 0, 0, 0, 16859086, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -6*x^17 +7*x^16 -55*x^15 +282*x^14 -1183*x^13 +6197*x^12 -44562*x^11 +50759*x^10 -349116*x^9 -50759*x^8 -44562*x^7 -6197*x^6 -1183*x^5 -282*x^4 -55*x^3 -7*x^2 -6*x -1) / (x^20 -16859086*x^10 +1). - Colin Barker, Dec 02 2013

a(n) = 16859086*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[583], 30]] (* Vincenzo Librandi, Jan 15 2014 *)

Crossrefs

Cf. A042116, A040558.

Sequence in context: A182622 A028423 A269912 * A335956 A179885 A217548

Adjacent sequences: A042114 A042115 A042116 * A042118 A042119 A042120

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved