Connected V-free graph

A V-free graph is a graph that doesn't have the induced subgraph \(K_{1,2}\); that is, the graph doesn't have three vertices \(a,b,c\) such that \(a\) is adjacent to both \(b\) and \(c\), but \(b,c\) are not adjacent.

How many connected V-free graphs having between 1 and 2016 vertices (inclusive) are there?


Hint: It's 1 April over here.

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