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A041787
Denominators of continued fraction convergents to sqrt(414).
2
1, 2, 3, 23, 49, 366, 415, 1196, 48255, 97706, 145961, 1119433, 2384827, 17813222, 20198049, 58209320, 2348570849, 4755351018, 7103921867, 54482804087, 116069530041, 866969514374, 983039044415, 2833047603204, 114304943172575, 231442933948354
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 48670, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^14 -2*x^13 +3*x^12 -23*x^11 +49*x^10 -366*x^9 +415*x^8 -1196*x^7 -415*x^6 -366*x^5 -49*x^4 -23*x^3 -3*x^2 -2*x -1) / (x^16 -48670*x^8 +1). - Colin Barker, Nov 24 2013
a(n) = 48670*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 24 2013
MATHEMATICA
Denominator[Convergents[Sqrt[414], 30]] (* Vincenzo Librandi, Dec 24 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 48670, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 2, 3, 23, 49, 366, 415, 1196, 48255, 97706, 145961, 1119433, 2384827, 17813222, 20198049, 58209320}, 30] (* Harvey P. Dale, Sep 27 2024 *)
PROG
(Magma) I:=[1, 2, 3, 23, 49, 366, 415, 1196, 48255, 97706, 145961, 1119433, 2384827, 17813222, 20198049, 58209320]; [n le 16 select I[n] else 48670*Self(n-8)-Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013
CROSSREFS
Sequence in context: A262838 A120366 A371310 * A143853 A195241 A090180
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 24 2013
STATUS
approved