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A042087
Denominators of continued fraction convergents to sqrt(567).
2
1, 1, 5, 16, 69, 85, 3979, 4064, 20235, 64769, 279311, 344080, 16106991, 16451071, 81911275, 262184896, 1130650859, 1392835755, 65201095589, 66593931344, 331576820965, 1061324394239, 4576874397921, 5638198792160, 263934018837281, 269572217629441
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,4048,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^10 -x^9 +5*x^8 -16*x^7 +69*x^6 -85*x^5 -69*x^4 -16*x^3 -5*x^2 -x -1) / ((x^4 -16*x^2 +1)*(x^8 +16*x^6 +255*x^4 +16*x^2 +1)). - Colin Barker, Dec 01 2013
a(n) = 4048*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Jan 14 2014
MATHEMATICA
Denominator[Convergents[Sqrt[567], 30]] (* Vincenzo Librandi, Jan 14 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 4048, 0, 0, 0, 0, 0, -1}, {1, 1, 5, 16, 69, 85, 3979, 4064, 20235, 64769, 279311, 344080}, 40] (* Harvey P. Dale, Nov 24 2022 *)
PROG
(Magma) I:=[1, 1, 5, 16, 69, 85, 3979, 4064, 20235, 64769, 279311, 344080]; [n le 12 select I[n] else 4048*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Jan 14 2014
CROSSREFS
Sequence in context: A027105 A254203 A220903 * A332470 A151465 A363299
KEYWORD
nonn,frac,easy
EXTENSIONS
More terms from Colin Barker, Dec 01 2013
STATUS
approved