A041940 Numerators of continued fraction convergents to sqrt(493).

22, 89, 111, 1199, 3708, 12323, 126938, 139261, 683982, 30234469, 121621858, 151856327, 1640185128, 5072411711, 16857420261, 173646614321, 190504034582, 935662752649, 41359665151138, 166374323357201, 207733988508339, 2243714208440591, 6938876613830112

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1367964,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^17 -22*x^16 +89*x^15 -111*x^14 +1199*x^13 -3708*x^12 +12323*x^11 -126938*x^10 +139261*x^9 +683982*x^8 +139261*x^7 +126938*x^6 +12323*x^5 +3708*x^4 +1199*x^3 +111*x^2 +89*x +22) / ((x^6 +111*x^3 -1)*(x^12 -111*x^9 +12322*x^6 +111*x^3 +1)). - Colin Barker, Nov 27 2013

Mathematica

Numerator[Convergents[Sqrt[493], 30]] (* Vincenzo Librandi, Nov 12 2013 *)

Crossrefs

Cf. A041941, A040470.

Sequence in context: A298443 A197720 A195323 * A041942 A231265 A041944

Adjacent sequences: A041937 A041938 A041939 * A041941 A041942 A041943

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved