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A041077
Denominators of continued fraction convergents to sqrt(45).
3
1, 1, 3, 7, 17, 24, 305, 329, 963, 2255, 5473, 7728, 98209, 105937, 310083, 726103, 1762289, 2488392, 31622993, 34111385, 99845763, 233802911, 567451585, 801254496, 10182505537, 10983760033, 32150025603, 75283811239, 182717648081, 258001459320, 3278735159921
OFFSET
0,3
LINKS
FORMULA
a(n) = 322*a(n-6)-a(n-12). G.f.: -(x^10-x^9+3*x^8-7*x^7+17*x^6-24*x^5-17*x^4-7*x^3-3*x^2-x-1)/((x^2-3*x+1)*(x^2+3*x+1)*(x^4-3*x^3+8*x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)). [Colin Barker, Jul 18 2012]
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[45], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*)
Denominator[Convergents[Sqrt[45], 30]] (* Vincenzo Librandi, Oct 24 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 322, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 7, 17, 24, 305, 329, 963, 2255, 5473, 7728}, 40] (* Harvey P. Dale, Jun 11 2022 *)
CROSSREFS
Sequence in context: A127176 A100343 A085396 * A041663 A042825 A076033
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Oct 24 2013
STATUS
approved