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A041880
Numerators of continued fraction convergents to sqrt(462).
2
21, 43, 1827, 3697, 157101, 317899, 13508859, 27335617, 1161604773, 2350545163, 99884501619, 202119548401, 8588905534461, 17379930617323, 738545991462027, 1494471913541377, 63506366360199861, 128507204633941099
OFFSET
0,1
FORMULA
G.f.: (21 +43*x +21*x^2 -x^3)/(1 -86*x^2 +x^4). - Vincenzo Librandi, Nov 11 2013
a(n) = 86*a(n-2) -a(n-4). - Vincenzo Librandi, Nov 11 2013
MATHEMATICA
Numerator[Convergents[Sqrt[462], 30]] (* or *) CoefficientList[Series[(21 + 43 x + 21 x^2 - x^3)/(1 - 86 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 11 2013 *)
LinearRecurrence[{0, 86, 0, -1}, {21, 43, 1827, 3697}, 30] (* Harvey P. Dale, Jul 25 2015 *)
PROG
(Magma) I:=[21, 43, 1827, 3697]; [n le 4 select I[n] else 86*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 11 2013
CROSSREFS
Cf. A041881.
Sequence in context: A041872 A041876 A041878 * A359880 A063319 A120071
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved