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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: A262079 A222009 A336297 * A261944 A142729 A167215 Adjacent sequences:  A041446 A041447 A041448 * A041450 A041451 A041452 KEYWORD nonn,frac,easy AUTHOR EXTENSIONS More terms from Colin Barker, Nov 17 2013 STATUS approved

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Last modified September 18 10:31 EDT 2020. Contains 337166 sequences. (Running on oeis4.)