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A042298 Numerators of continued fraction convergents to sqrt(675). 2
25, 26, 1325, 1351, 68875, 70226, 3580175, 3650401, 186100225, 189750626, 9673631525, 9863382151, 502842739075, 512706121226, 26138148800375, 26650854921601, 1358680894880425, 1385331749802026, 70625268384981725, 72010600134783751, 3671155275124169275 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
G.f.: -(x^3-25*x^2-26*x-25) / (x^4-52*x^2+1). - Vincenzo Librandi, Nov 21 2013, simplified by Colin Barker, Dec 28 2013
a(n) = 52*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 21 2013, simplified by Colin Barker, Dec 28 2013
MATHEMATICA
Numerator[Convergents[Sqrt[675], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 1325 x^2 + 1351 x^3 + 1325 x^4 - 26 x^5 + 25 x^6 - x^7)/(1 - 2702 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)
PROG
(Magma) I:=[25, 26, 1325, 1351, 68875, 70226, 3580175, 3650401]; [n le 8 select I[n] else 2702*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013
CROSSREFS
Sequence in context: A041311 A042296 A042297 * A157091 A070662 A350181
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Dec 28 2013
STATUS
approved

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Last modified June 21 03:54 EDT 2024. Contains 373540 sequences. (Running on oeis4.)