A041941 Denominators of continued fraction convergents to sqrt(493).

1, 4, 5, 54, 167, 555, 5717, 6272, 30805, 1361692, 5477573, 6839265, 73870223, 228449934, 759220025, 7820650184, 8579870209, 42140131020, 1862745635089, 7493122671376, 9355868306465, 101051805736026, 312511285514543, 1038585662279655, 10698367908311093

Offset

0,2

Links

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

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

Formula

G.f.: -(x^16 -4*x^15 +5*x^14 -54*x^13 +167*x^12 -555*x^11 +5717*x^10 -6272*x^9 +30805*x^8 +6272*x^7 +5717*x^6 +555*x^5 +167*x^4 +54*x^3 +5*x^2 +4*x +1) / ((x^6 +111*x^3 -1)*(x^12 -111*x^9 +12322*x^6 +111*x^3 +1)). - Colin Barker, Nov 27 2013

Mathematica

Denominator[Convergents[Sqrt[493], 30]] (* Harvey P. Dale, Mar 25 2013 *)
CoefficientList[Series[-(x^16 - 4 x^15 + 5 x^14 - 54 x^13 + 167 x^12 - 555 x^11 + 5717 x^10 - 6272 x^9 + 30805 x^8 + 6272 x^7 + 5717 x^6 + 555 x^5 + 167 x^4 + 54 x^3 + 5 x^2 + 4 x + 1)/((x^6 + 111 x^3 - 1) (x^12 - 111 x^9 + 12322 x^6 + 111 x^3 + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 27 2013 *)

Crossrefs

Cf. A041940, A040470.

Sequence in context: A135799 A226648 A335797 * A220534 A368018 A341575

Adjacent sequences: A041938 A041939 A041940 * A041942 A041943 A041944

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved