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A041449 Denominators of continued fraction convergents to sqrt(240). 3
1, 2, 61, 124, 3781, 7686, 234361, 476408, 14526601, 29529610, 900414901, 1830359412, 55811197261, 113452753934, 3459393815281, 7032240384496, 214426605350161, 435885451084818, 13290990137894701, 27017865726874220, 823826961944121301, 1674671789615116822 (list; graph; refs; listen; history; text; internal format)
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: A130411 A262079 A222009 * 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

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Last modified June 1 18:43 EDT 2020. Contains 334762 sequences. (Running on oeis4.)