A042079 Denominators of continued fraction convergents to sqrt(563).

1, 1, 3, 4, 11, 257, 525, 782, 2089, 2871, 134155, 137026, 408207, 545233, 1498673, 35014712, 71528097, 106542809, 284613715, 391156524, 18277813819, 18668970343, 55615754505, 74284724848, 204185204201, 4770544421471, 9745274047143, 14515818468614

Offset

0,3

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, 136244, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +3*x^16 -4*x^15 +11*x^14 -257*x^13 +525*x^12 -782*x^11 +2089*x^10 -2871*x^9 -2089*x^8 -782*x^7 -525*x^6 -257*x^5 -11*x^4 -4*x^3 -3*x^2 -x -1) / (x^20 -136244*x^10 +1). - Colin Barker, Dec 01 2013

a(n) = 136244*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Jan 14 2014

Mathematica

Denominator[Convergents[Sqrt[563], 30]] (* Vincenzo Librandi, Jan 14 2014 *)

Crossrefs

Cf. A042078, A040539.

Sequence in context: A343931 A041299 A001112 * A045826 A346471 A084200

Adjacent sequences: A042076 A042077 A042078 * A042080 A042081 A042082

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 01 2013

Status

approved