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A042106
Numerators of continued fraction convergents to sqrt(578).
2
24, 577, 27720, 665857, 31988856, 768398401, 36915112104, 886731088897, 42600007379160, 1023286908188737, 49160371600438536, 1180872205318713601, 56731026226898691384, 1362725501650887306817, 65467555105469489418600
OFFSET
0,1
FORMULA
G.f.: -(x^3 - 24*x^2 - 577*x - 24)/(x^4 - 1154*x^2 + 1). - Vincenzo Librandi, Nov 16 2013
a(n) = 1154*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 16 2013
MATHEMATICA
Numerator[Convergents[Sqrt[578], 30]] (* or *) CoefficientList[Series[-(x^3 - 24 x^2 - 577 x - 24)/(x^4 - 1154 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)
LinearRecurrence[{0, 1154, 0, -1}, {24, 577, 27720, 665857}, 20] (* Harvey P. Dale, Jul 04 2015 *)
PROG
(Magma) I:=[24, 577, 27720, 665857]; [n le 4 select I[n] else 1154*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013
CROSSREFS
Cf. A042107.
Sequence in context: A268027 A009968 A041265 * A158637 A179059 A334281
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved