Zero followed by Fibonacci(2*n+1) for n = 1, 2, 3,....
0, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229, 1346269, 3524578, 9227465, 24157817, 63245986, 165580141, 433494437, 1134903170, 2971215073, 7778742049, 20365011074, 53316291173, 139583862445, 365435296162, 956722026041
0
Let M be the symmetric matrix whose elements are Fibonacci(i + j) for i,j = 0,..,n. This sequence is the largest eigenvalue of matrix M, rounded up. When the first row and column are ignored, then the sequence produces Fibonacci(2*n), A001906.
T. D. Noe, Plot of 201 terms
T. D. Noe, Table of 201 terms
Eric W. Weisstein, MathWorld: Fibonacci Number
(Mma) Join[{0}, Table[Fibonacci[2*n + 1], {n, 30}]]
Cf. S000624.
nonn
T. D. Noe, May 11 2015