A041506 Numerators of continued fraction convergents to sqrt(270).

16, 33, 115, 723, 2284, 5291, 171596, 348483, 1217045, 7650753, 24169304, 55989361, 1815828856, 3687647073, 12878770075, 80960267523, 255759572644, 592479412811, 19215100782596, 39022680978003, 136283143716605, 856721543277633, 2706447773549504

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,10582,0,0,0,0,0,-1).

Formula

G.f.: -(x^11 -16*x^10 +33*x^9 -115*x^8 +723*x^7 -2284*x^6 -5291*x^5 -2284*x^4 -723*x^3 -115*x^2 -33*x -16) / ((x^4 -22*x^2 +1)*(x^8 +22*x^6 +483*x^4 +22*x^2 +1)). - Colin Barker, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[270], 30]] (* Vincenzo Librandi, Nov 03 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 10582, 0, 0, 0, 0, 0, -1}, {16, 33, 115, 723, 2284, 5291, 171596, 348483, 1217045, 7650753, 24169304, 55989361}, 30] (* Harvey P. Dale, Dec 25 2019 *)

Crossrefs

Cf. A041507.

Sequence in context: A198275 A041504 A275252 * A041508 A144533 A041510

Adjacent sequences: A041503 A041504 A041505 * A041507 A041508 A041509

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 10 2013

Status

approved