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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
OFFSET
0,2
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
Sequence in context: A222009 A351728 A336297 * A261944 A142729 A167215
KEYWORD
nonn,frac,easy
EXTENSIONS
More terms from Colin Barker, Nov 17 2013
STATUS
approved