The terms of A000278, the sequence defined by h 0=0, hp 1, and h n+2=h n+1+h n 2, count the trees in certain recursively defined forests. We show that for n large, h n is approximately A sqrt(2)n for n even and h n is approximately B sqrt(2)n for n odd, with A,B > 1 and A not equal to B, and we give estimates of A and B: A is 1.436 ±.001 and B is 1.452 ±.001. The doubly exponential growth of the sequence is not surprising (see, for example, [AS]) but the dependence of the growth on the parity of the subscript is more interesting. Numerical and analytical investigation of similar sequences suggests a possible generalization of this result to a large class of such recursions.
|Original language||English (US)|
|Journal||Journal of Integer Sequences|
|State||Published - Dec 1 1998|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics