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A041427
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Denominators of continued fraction convergents to sqrt(229).
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10
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1, 7, 8, 15, 113, 3405, 23948, 27353, 51301, 386460, 11645101, 81902167, 93547268, 175449435, 1321693313, 39826248825, 280105435088, 319931683913, 600037119001, 4520191516920, 136205782626601, 957960669903127, 1094166452529728, 2052127122432855
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OFFSET
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0,2
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COMMENTS
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The a(n) terms of this sequence can be constructed with the terms of sequence A154597. For the terms of the periodical sequence of the continued fraction for sqrt(229) see A040213. We observe that its period is five. - Johannes W. Meijer, Jun 12 2010
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 3420, 0, 0, 0, 0, 1).
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FORMULA
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a(5*n) = A154597(3*n+1), a(5*n+1) = (A154597(3*n+2) - A154597(3*n+1))/2, a(5*n+2) = (A154597(3*n+2) + A154597(3*n+1))/2, a(5*n+3) = A154597(3*n+2) and a(5*n+4) = A154597(3*n+3)/2. - Johannes W. Meijer, Jun 12 2010
G.f.: -(x^8 -7*x^7 +8*x^6 -15*x^5 +113*x^4 +15*x^3 +8*x^2 +7*x +1) / (x^10 +3420*x^5 -1). - Colin Barker, Nov 12 2013
a(n) = 3420*a(n-5) + a(n-10) for n>9. - Vincenzo Librandi, Dec 17 2013
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MATHEMATICA
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Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[229], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
Denominator[Convergents[Sqrt[229], 30]] (* Vincenzo Librandi, Dec 17 2013 *)
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PROG
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(MAGMA) I:=[1, 7, 8, 15, 113, 3405, 23948, 27353, 51301, 386460]; [n le 10 select I[n] else 3420*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013
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CROSSREFS
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Cf. A041426, A166125, A040213, A041019, A041047, A041091, A041151, A041227, A041319, A041427 and A041551.
Sequence in context: A084377 A041675 A041098 * A042755 A093083 A323418
Adjacent sequences: A041424 A041425 A041426 * A041428 A041429 A041430
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KEYWORD
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nonn,easy,frac
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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