### Abstract

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) |
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Journal | Journal of Integer Sequences |

Volume | 1 |

State | Published - Dec 1 1998 |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

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## Cite this

*Journal of Integer Sequences*,

*1*.