A041769 Denominators of continued fraction convergents to sqrt(405).

1, 8, 321, 2576, 103361, 829464, 33281921, 267084832, 10716675201, 86000486440, 3450736132801, 27691889548848, 1111126318086721, 8916702434242616, 357779223687791361, 2871150491936573504, 115203798901150731521, 924501541701142425672

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,322,0,-1).

Formula

G.f.: -(x^2-8*x-1) / ((x^2-18*x+1)*(x^2+18*x+1)). - Colin Barker, Nov 24 2013

a(n) = 322*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[405], 30]] (* Vincenzo Librandi, Dec 24 2013 *)

Prog

(Magma) I:=[1, 8, 321, 2576]; [n le 4 select I[n] else 322*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041768, A040384.

Sequence in context: A227657 A057982 A308615 * A209277 A182275 A171248

Adjacent sequences: A041766 A041767 A041768 * A041770 A041771 A041772

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 24 2013

Status

approved