A041838 Numerators of continued fraction convergents to sqrt(440).

20, 21, 860, 881, 36100, 36981, 1515340, 1552321, 63608180, 65160501, 2670028220, 2735188721, 112077577060, 114812765781, 4704588208300, 4819400974081, 197480627171540, 202300028145621, 8289481752996380

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,42,0,-1).

Formula

G.f.: (20 + 21*x + 20*x^2 - x^3)/(1 - 42*x^2 + x^4). - Vincenzo Librandi, Nov 10 2013

a(n) = 42*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[440], 30]] (* or *) CoefficientList[Series[(20 + 21 x + 20 x^2 - x^3)/(1 - 42 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 10 2013 *)

Prog

(Magma) I:=[20, 21, 860, 881]; [n le 8 select I[n] else 42*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 10 2013

Crossrefs

Cf. A041839.

Sequence in context: A302205 A041836 A041837 * A128356 A109212 A259742

Adjacent sequences: A041835 A041836 A041837 * A041839 A041840 A041841

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved