login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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