|
|
A103433
|
|
a(n) = Sum_{i=1..n} Fibonacci(2i-1)^2.
|
|
6
|
|
|
0, 1, 5, 30, 199, 1355, 9276, 63565, 435665, 2986074, 20466835, 140281751, 961505400, 6590256025, 45170286749, 309601751190, 2122041971551, 14544692049635, 99690802375860, 683290924581349, 4683345669693545
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
REFERENCES
|
A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 234.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(1-4*x+x^2) / ((1-7*x+x^2)(1-x)^2).
a(n) = (1/5)*(Fibonacci(4n) + 2n).
a(n) = (floor(5*n*phi) + 4*Fibonacci(4*n))/20, where phi =(1+sqrt(5))/2. - Gary Detlefs, Mar 10 2011
a(n) = (8*(n+2)*(Sum_{k=1..n} 1/(2*k^2 + 6*k + 4)) + Fibonacci(4*n))/5. - Gary Detlefs, Dec 07 2011
a(n) = | Sum_{i=0..2n-1} (-1)^i*F(i)*F(i+1) |, where F(n) = Fibonacci numbers (A000045). - Rigoberto Florez, May 04 2019
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) [(1/5)*(Fibonacci(4*n)+2*n): n in [0..50]]; // Vincenzo Librandi, Apr 20 2011
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|