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A041121
Denominators of continued fraction convergents to sqrt(69).
2
1, 3, 10, 13, 62, 75, 287, 936, 15263, 46725, 155438, 202163, 964090, 1166253, 4462849, 14554800, 237339649, 726573747, 2417060890, 3143634637, 14991599438, 18135234075, 69397301663, 226327139064, 3690631526687, 11298221719125, 37585296684062, 48883518403187
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,15550,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^14 -3*x^13 +10*x^12 -13*x^11 +62*x^10 -75*x^9 +287*x^8 -936*x^7 -287*x^6 -75*x^5 -62*x^4 -13*x^3 -10*x^2 -3*x -1) / (x^16 -15550*x^8 +1). - Colin Barker, Nov 13 2013
a(n) = 15550*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 11 2013
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[69], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
Denominator[Convergents[Sqrt[69], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 15550, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 3, 10, 13, 62, 75, 287, 936, 15263, 46725, 155438, 202163, 964090, 1166253, 4462849, 14554800}, 30] (* Harvey P. Dale, Oct 18 2015 *)
PROG
(Magma) I:=[1, 3, 10, 13, 62, 75, 287, 936, 15263, 46725, 155438, 202163, 964090, 1166253, 4462849, 14554800]; [n le 16 select I[n] else 15550*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 13 2013
STATUS
approved