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A041798
Numerators of continued fraction convergents to sqrt(420).
2
20, 41, 1660, 3361, 136100, 275561, 11158540, 22592641, 914864180, 1852321001, 75007704220, 151867729441, 6149716881860, 12451301493161, 504201776608300, 1020854854709761, 41338395964998740, 83697646784707241
OFFSET
0,1
FORMULA
G.f.: (20+41*x+20*x^2-x^3)/(1-82*x^2+x^4). - Vincenzo Librandi, Nov 09 2013
a(n) = 82*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 09 2013
MATHEMATICA
Numerator[Convergents[Sqrt[420], 30]] (* or *) CoefficientList[Series[(20 + 41 x + 20 x^2 - x^3)/(1 - 82 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 09 2013 *)
LinearRecurrence[{0, 82, 0, -1}, {20, 41, 1660, 3361}, 30] (* Harvey P. Dale, Dec 16 2017 *)
PROG
(Magma) I:=[20, 41, 1660, 3361]; [n le 4 select I[n] else 82*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 09 2013
CROSSREFS
Cf. A041799.
Sequence in context: A041792 A041794 A041796 * A132762 A075228 A256102
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved