A041505 Denominators of continued fraction convergents to sqrt(269).

1, 2, 5, 162, 329, 820, 26569, 53958, 134485, 4357478, 8849441, 22056360, 714652961, 1451362282, 3617377525, 117207443082, 238032263689, 593271970460, 19222735318409, 39038742607278, 97300220532965, 3152645799662158, 6402591819857281, 15957829439376720

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,164,0,0,1).

Formula

G.f.: -(x^4-2*x^3+5*x^2+2*x+1) / (x^6+164*x^3-1). - Colin Barker, Nov 18 2013

a(n) = 164*a(n-3) + a(n-6) for n>5. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[269], 30]] (* Vincenzo Librandi, Dec 19 2013 *)
LinearRecurrence[{0, 0, 164, 0, 0, 1}, {1, 2, 5, 162, 329, 820}, 30] (* Harvey P. Dale, Jan 22 2019 *)

Prog

(Magma) I:=[1, 2, 5, 162, 329, 820]; [n le 6 select I[n] else 164*Self(n-3)+Self(n-6): n in [1..30]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041504, A040252.

Sequence in context: A062611 A263413 A270585 * A116629 A124275 A013130

Adjacent sequences: A041502 A041503 A041504 * A041506 A041507 A041508

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved