A041943 Denominators of continued fraction convergents to sqrt(494).

1, 4, 9, 22, 31, 84, 115, 314, 743, 3286, 145327, 584594, 1314515, 3213624, 4528139, 12269902, 16798041, 45865984, 108530009, 479986020, 21227914889, 85391645576, 192011206041, 469414057658, 661425263699, 1792264585056, 2453689848755, 6699644282566

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, 146070, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -4*x^17 +9*x^16 -22*x^15 +31*x^14 -84*x^13 +115*x^12 -314*x^11 +743*x^10 -3286*x^9 -743*x^8 -314*x^7 -115*x^6 -84*x^5 -31*x^4 -22*x^3 -9*x^2 -4*x -1) / (x^20 -146070*x^10 +1). - Colin Barker, Nov 27 2013

a(n) = 146070*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 27 2013

Mathematica

Denominator[Convergents[Sqrt[494], 30]] (* Vincenzo Librandi, Dec 27 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 146070, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 4, 9, 22, 31, 84, 115, 314, 743, 3286, 145327, 584594, 1314515, 3213624, 4528139, 12269902, 16798041, 45865984, 108530009, 479986020}, 30] (* Harvey P. Dale, May 21 2018 *)

Crossrefs

Cf. A041942, A040471.

Sequence in context: A048391 A343322 A041743 * A158140 A290647 A105314

Adjacent sequences: A041940 A041941 A041942 * A041944 A041945 A041946

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved