A041449 Denominators of continued fraction convergents to sqrt(240).

1, 2, 61, 124, 3781, 7686, 234361, 476408, 14526601, 29529610, 900414901, 1830359412, 55811197261, 113452753934, 3459393815281, 7032240384496, 214426605350161, 435885451084818, 13290990137894701, 27017865726874220, 823826961944121301, 1674671789615116822

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,62,0,-1).

Formula

G.f.: -(x^2-2*x-1) / ((x^2-8*x+1)*(x^2+8*x+1)). - Colin Barker, Nov 17 2013

a(n) = 62*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 18 2013

From Gerry Martens, Jul 11 2015: (Start)

Interspersion of 2 sequences [a0(n-1),a1(n-1)] for n>0:

a0(n) = sqrt(2+(31-8*sqrt(15))^(2*n+1)+(31+8*sqrt(15))^(2*n+1))/8.

a1(n) = 2*sum(i=0,n,a0(i)). (End)

Mathematica

Denominator[Convergents[Sqrt[240], 30]] (* Vincenzo Librandi, Dec 18 2013 *)
a0[n_] := Sqrt[2+(31-8*Sqrt[15])^(1+2*n)+(31+8*Sqrt[15])^(1+2*n)]/8 // Simplify
a1[n_] := 2*Sum[a0[i], {i, 0, n}]
Flatten[MapIndexed[{a0[#-1], a1[#-1]}&, Range[11]]] (* Gerry Martens, Jul 10 2015 *)

Prog

(Magma) I:=[1, 2, 61, 124]; [n le 4 select I[n] else 62*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041448, A040224.

Sequence in context: A222009 A351728 A336297 * A261944 A142729 A167215

Adjacent sequences: A041446 A041447 A041448 * A041450 A041451 A041452

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved