A041720 Numerators of continued fraction convergents to sqrt(380).

19, 39, 1501, 3041, 117059, 237159, 9129101, 18495361, 711952819, 1442400999, 55523190781, 112488782561, 4330096928099, 8772682638759, 337692037200941, 684156757040641, 26335648804745299, 53355454366531239

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,78,0,-1).

Formula

G.f.: (19+39*x+19*x^2-x^3)/(1-78*x^2+x^4). - Vincenzo Librandi, Nov 07 2013

a(n) = 78*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 07 2013

Mathematica

Numerator[Convergents[Sqrt[380], 30]] (* or *) CoefficientList[Series[(19 + 39 x + 19 x^2 - x^3)/(1 - 78 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 07 2013 *)

Prog

(Magma) I:=[19, 39, 1501, 3041]; [n le 4 select I[n] else 78*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 07 2013

Crossrefs

Cf. A041721.

Sequence in context: A041714 A041716 A041718 * A098850 A264537 A164078

Adjacent sequences: A041717 A041718 A041719 * A041721 A041722 A041723

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved