A144978 A005195(n) - A005195(n-2).

1, 1, 2, 4, 7, 14, 27, 56, 116, 253, 557, 1272, 2948, 6998, 16856, 41306, 102449, 257294, 652566, 1670679, 4311109, 11206278, 29316294, 77144518, 204072054, 542446974, 1448230644, 3882179984, 10445521740, 28202158173, 76387639678

Offset: 1

Author

Washington Bomfim, Sep 28 2008

Keywords

• nonn

Comments

a(n) is the number of forests with n unlabeled nodes without trees of order 2. This follows from the fact that for n>=2 A005195(n-2) counts the forests of order n with one or more trees of order 2.

The unique forest of order 1 is an isolated vertex, so a(1)=1. For n>=2, a(n) - a(n-1) counts forests of order n with trees of order >=3.

A005195(n) - A005195(n-3) counts forests of order n without trees of order 3.

Examples

			a(5) = 7 since the only options are: 3 trees of order 5; 2 forests composed by trees of orders 4 and l; one forest with trees of orders [3 1 1]; and one forest with five isolated nodes.
		

Crossrefs

Cf. A005195, A000055(trees).