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A041127
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Denominators of continued fraction convergents to sqrt(72).
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2
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1, 2, 33, 68, 1121, 2310, 38081, 78472, 1293633, 2665738, 43945441, 90556620, 1492851361, 3076259342, 50713000833, 104502261008, 1722749176961, 3550000614930, 58522759015841, 120595518646612, 1988051057361633, 4096697633369878, 67535213191279681
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: -(x^2-2*x-1) / ((x^2-6*x+1)*(x^2+6*x+1)). - Colin Barker, Nov 13 2013
Interspersion of 2 sequences [a0(n),a1(n)] for n>0:
a0(n) = ((3+2*sqrt(2))/(17+12*sqrt(2))^n+(3-2*sqrt(2))*(17+12*sqrt(2))^n)/6.
a1(n) = (-1/(17+12*sqrt(2))^n+(17+12*sqrt(2))^n)/(12*sqrt(2)). (End)
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MATHEMATICA
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CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 34 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
a0[n_] := ((3+2*Sqrt[2])/(17+12*Sqrt[2])^n+(3-2*Sqrt[2])*(17+ 12*Sqrt[2])^n)/6 // Simplify
a1[n_] := (-1/(17+12*Sqrt[2])^n+(17+12*Sqrt[2])^n)/(12*Sqrt[2]) // FullSimplify
Flatten[MapIndexed[{a0[#], a1[#]}&, Range[20]]] (* Gerry Martens, Jul 10 2015 *)
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PROG
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(PARI) a(n)=my(v=contfrac(sqrt(72), n), s=v[n]); forstep(k=n-1, 1, -1, s=v[k]+1/s); denominator(s) \\ Charles R Greathouse IV, Jul 05 2011
(Magma) I:=[1, 2, 33, 68]; [n le 4 select I[n] else 34*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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