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URL: https://oeis.org/A041227

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A041227
Denominators of continued fraction convergents to sqrt(125).
10
1, 5, 6, 11, 61, 1353, 6826, 8179, 15005, 83204, 1845493, 9310669, 11156162, 20466831, 113490317, 2517253805, 12699759342, 15217013147, 27916772489, 154800875592, 3433536035513, 17322481053157, 20756017088670, 38078498141827, 211148507797805
OFFSET
0,2
COMMENTS
The a(n) terms of this sequence can be constructed with the terms of sequence A049666. For the terms of the periodical sequence of the continued fraction for sqrt(125) see A010186. We observe that its period is five. - Johannes W. Meijer, Jun 12 2010
LINKS
FORMULA
a(5*n) = A049666(3*n+1), a(5*n+1) = (A049666(3*n+2) - A049666(3*n+1))/2, a(5*n+2) = (A049666(3*n+2)+A049666(3*n+1))/2, a(5*n+3):= A049666(3*n+2) and a(5*n+4) = A049666(3*n+3)/2. - Johannes W. Meijer, Jun 12 2010
G.f.: -(x^8 -5*x^7 +6*x^6 -11*x^5 +61*x^4 +11*x^3 +6*x^2 +5*x +1) / ((x^2 +4*x -1)*(x^4 -7*x^3 +19*x^2 -3*x +1)*(x^4 +3*x^3 +19*x^2 +7*x +1)). - Colin Barker, Nov 12 2013
a(n) = 1364*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 13 2013
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[125], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
Denominator[Convergents[Sqrt[125], 30]] (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 0, 0, 0, 1364, 0, 0, 0, 0, 1}, {1, 5, 6, 11, 61, 1353, 6826, 8179, 15005, 83204}, 30] (* Harvey P. Dale, Apr 29 2022 *)
PROG
(Magma) I:=[1, 5, 6, 11, 61, 1353, 6826, 8179, 15005, 83204]; [n le 10 select I[n] else 1364*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013
KEYWORD
nonn,frac,easy
STATUS
approved