A214650 Number of distinct connected unicyclic bipartite graphs with n vertices.

0, 0, 0, 1, 1, 5, 10, 34, 85, 254, 690, 1997, 5582, 15975, 45244, 129254, 368215, 1052961, 3010169, 8622273, 24709964, 70902886, 203594559, 585163116, 1683079071, 4844758076, 13955265122, 40225474849, 116021495035, 334843170810, 966929417619, 2793756318793

Offset: 1

Author

David Bevan, Jul 24 2012

Keywords

• nonn

Comments

The graphs also have n edges.

Examples

			a(5)=1, a 4-cycle plus a pendant edge.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Unicyclic Graph

Crossrefs

Cf. A001429.

Programs

PARI

\\ TreeGf gives gf of A000081
TreeGf(N)={my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*A[d]) * A[n-k+1] ) ); x*Ser(A)}
seq(n)={concat([0,0,0], if(n<4, [], my(t=TreeGf(n-2)); my(g(e)=subst(t + O(x*x^(n\e)), x, x^e) + O(x*x^n)); Vec(sum(k=2, n\2, sumdiv(2*k, d, eulerphi(d)*g(d)^(2*k/d))/k + (g(1)^2+g(2))*g(2)^(k-1))/4)))} \\ Andrew Howroyd, May 22 2018

Extensions

Terms a(16) and beyond from Andrew Howroyd, May 22 2018