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A041031
Denominators of continued fraction convergents to sqrt(20).
2
1, 2, 17, 36, 305, 646, 5473, 11592, 98209, 208010, 1762289, 3732588, 31622993, 66978574, 567451585, 1201881744, 10182505537, 21566892818, 182717648081, 387002188980, 3278735159921, 6944472508822
OFFSET
0,2
FORMULA
G.f.: (1+2*x-x^2)/(1-18*x^2+x^4). - Colin Barker, Jan 01 2012
From Gerry Martens, Jul 11 2015: (Start)
Interspersion of 2 sequences [a0(n),a1(n)] for n>0:
a0(n) = ((5+2*sqrt(5))/(9+4*sqrt(5))^n+(5-2*sqrt(5))*(9+4*sqrt(5))^n)/10.
a1(n) = (-1/(9+4*sqrt(5))^n+(9+4*sqrt(5))^n)/(4*sqrt(5)). (End)
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[20], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
a0[n_] := ((5+2*Sqrt[5])/(9+4*Sqrt[5])^n+(5-2*Sqrt[5])*(9+4*Sqrt[5])^n)/10 //Simplify
a1[n_] := (-1/(9+4*Sqrt[5])^n+(9+4*Sqrt[5])^n)/(4*Sqrt[5]) //Simplify
Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *)
CROSSREFS
Cf. A010476, A040015, A041030 (numerators).
Sequence in context: A342485 A342487 A342613 * A041965 A095075 A307161
KEYWORD
nonn,cofr,frac,easy
STATUS
approved