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A041015
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Denominators of continued fraction convergents to sqrt(11).
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2
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1, 3, 19, 60, 379, 1197, 7561, 23880, 150841, 476403, 3009259, 9504180, 60034339, 189607197, 1197677521, 3782639760, 23893516081, 75463188003, 476672644099, 1505481120300, 9509559365899, 30034159217997
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Sqrt(11) = 3 + continued fraction [3, 6, 3, 6, 3, 6,...] = 6/2 + 6/19 + 6/(19*379) + 6/(379*7561)... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 21 2007
Let X = the 2 X 2 matrix [1, 6; 3, 19], then X^n * [1, 0] = [a(n+1), a(n+2)]; e.g. X^3 * [1, 0] = [379, 1197] = [a(4), a(5)]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 21 2007
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FORMULA
| Empirical G.f.: (1+3*x-x^2)/(1-20*x^2+x^4). [Colin Barker, Dec 31 2011]
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MATHEMATICA
| Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[11], n]]], {n, 1, 50}] (*From Vladimir Joseph Stephan Orlovsky, Mar 16 2011*)
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CROSSREFS
| Cf. A041014.
Sequence in context: A164132 A106875 A012863 * A185448 A114250 A178747
Adjacent sequences: A041012 A041013 A041014 * A041016 A041017 A041018
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KEYWORD
| nonn,cofr,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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