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 A215043 a(n) = F(12*n)/(24*L(2*n)), n >= 0, with F = A000045 (Fibonacci) and L = A000032 (Lucas). 2
 0, 2, 276, 34561, 4261992, 524393210, 64499742738, 7933009283134, 975696814205904, 120002796170968643, 14759368609635548580, 1815282342961539780022, 223264968937188026209956, 27459775899111901985784506 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 24*a(n) is the third example for the Riordan transition matrix introduced in a comment on A078812 (with offset [0,0]). Take there l -> n, n -> 2. See the second formula below. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 Index entries for linear recurrences with constant coefficients, signature (144,-2640,6930,-2640,144,-1). FORMULA a(n) = F(12*n)/(24*L(2*n)), n >= 0, with F = A000045 (Fibonacci) and L = A000032 (Lucas). a(n) = 3*F(2*n) + 20*F(2*n)^3 + 25*F(2*n)^5, n >= 0 (see the comment above). O.g.f.: x*(2 - 12*x + 97*x^2 - 12*x^3 + 2*x^4)/((1 - 3*x + x^2)*(1 - 18*x + x^2)*(1 - 123*x + x^2)). From the o.g.f.s for the sequences appearing in the preceding formula, see A001906, A215039 and A215044. a(n) = (L(8*n) + 1)*F(2*n)/24. - Ehren Metcalfe, Jun 04 2019 MATHEMATICA Table[Fibonacci[12*n]/(24*LucasL[2*n]), {n, 0, 15}] (* G. C. Greubel, Jun 30 2019 *) PROG (MAGMA) [Fibonacci(12*n)/(24*Lucas(2*n)): n in [0..15]] // Vincenzo Librandi, Sep 02 2012 (PARI) lucas(n) = fibonacci(n+1) + fibonacci(n-1); vector(15, n, n--; fibonacci(12*n)/(24*lucas(2*n))) \\ G. C. Greubel, Jun 30 2019 (Sage) [fibonacci(12*n)/(24*lucas_number2(2*n, 1, -1)) for n in (0..15)] # G. C. Greubel, Jun 30 2019 CROSSREFS Cf. A215042 (for F(8*n)/L(2*n)). Sequence in context: A237993 A174710 A200168 * A119553 A093938 A172374 Adjacent sequences:  A215040 A215041 A215042 * A215044 A215045 A215046 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2012 STATUS approved

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Last modified September 16 18:24 EDT 2019. Contains 327116 sequences. (Running on oeis4.)