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A041944 Numerators of continued fraction convergents to sqrt(495). 2
22, 89, 3938, 15841, 700942, 2819609, 124763738, 501874561, 22207244422, 89330852249, 3952764743378, 15900389825761, 703569917076862, 2830180058133209, 125231492474938058, 503756149957885441 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
G.f.: (22 + 89*x + 22*x^2 - x^3)/(1 - 178*x^2 + x^4). - Vincenzo Librandi, Nov 12 2013
a(n) = 178*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 12 2013
MATHEMATICA
Numerator[Convergents[Sqrt[495], 30]] (* or *) CoefficientList[Series[(22 + 89 x + 22 x^2 - x^3)/(1 - 178 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *)
LinearRecurrence[{0, 178, 0, -1}, {22, 89, 3938, 15841}, 30] (* Harvey P. Dale, Dec 07 2015 *)
PROG
(Magma) I:=[22, 89, 3938, 15841]; [n le 4 select I[n] else 178*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 12 2013
CROSSREFS
Cf. A041945.
Sequence in context: A041940 A041942 A231265 * A230357 A145769 A256152
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)