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) = 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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 31 2012
STATUS
approved