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A041125 Denominators of continued fraction convergents to sqrt(71). 2
1, 2, 5, 7, 54, 61, 176, 413, 6784, 13981, 34746, 48727, 375835, 424562, 1224959, 2874480, 47216639, 97307758, 241832155, 339139913, 2615811546, 2954951459, 8525714464, 20006380387, 328627800656, 677261981699, 1683151764054, 2360413745753, 18206047984325 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,6960,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^14 -2*x^13 +5*x^12 -7*x^11 +54*x^10 -61*x^9 +176*x^8 -413*x^7 -176*x^6 -61*x^5 -54*x^4 -7*x^3 -5*x^2 -2*x -1) / (x^16 -6960*x^8 +1). - Colin Barker, Nov 13 2013
a(n) = 6960*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 11 2013
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[71], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
Denominator[Convergents[Sqrt[71], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 6960, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 2, 5, 7, 54, 61, 176, 413, 6784, 13981, 34746, 48727, 375835, 424562, 1224959, 2874480}, 30] (* Harvey P. Dale, Apr 09 2022 *)
PROG
(Magma) I:=[1, 2, 5, 7, 54, 61, 176, 413, 6784, 13981, 34746, 48727, 375835, 424562, 1224959, 2874480]; [n le 16 select I[n] else 6960*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
CROSSREFS
Sequence in context: A041653 A182785 A358381 * A293592 A042257 A343833
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 13 2013
STATUS
approved

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Last modified June 20 23:18 EDT 2024. Contains 373535 sequences. (Running on oeis4.)