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A041257
Denominators of continued fraction convergents to sqrt(140).
2
1, 1, 5, 6, 137, 143, 709, 852, 19453, 20305, 100673, 120978, 2762189, 2883167, 14294857, 17178024, 392211385, 409389409, 2029769021, 2439158430, 55691254481, 58130412911, 288212906125, 346343319036
OFFSET
0,3
FORMULA
G.f.: (1 +x +5*x^2 +6*x^3 -5*x^4 +x^5 -x^6)/(1 -142*x^4 +x^8). - Vincenzo Librandi, Dec 13 2013
a(n) = 142*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 13 2013
MATHEMATICA
Denominator[Convergents[Sqrt[140], 30]] (* or *) CoefficientList[Series[(1 + x + 5 x^2 + 6 x^3 - 5 x^4 + x^5 - x^6)/(1 - 142 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 13 2013 *)
PROG
(Magma) I:=[1, 1, 5, 6, 137, 143, 709, 852]; [n le 8 select I[n] else 142*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013
CROSSREFS
Cf. A041256.
Sequence in context: A065354 A078984 A266718 * A337465 A041411 A103089
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved