A069725 Number of nonisomorphic unrooted unicursal planar maps with n edges and two vertices of valency 1 (unicursal means that exactly two vertices are of odd valency; there is an Eulerian path).

1, 1, 3, 11, 62, 342, 2152, 13768, 91800, 622616, 4301792, 30100448, 213019072, 1521473984, 10954616064, 79420280064, 579300888960, 4248201302400, 31302536066560, 231638727063040

Offset

1,3

Comments

There is an easy formula.

Links

Table of n, a(n) for n=1..20.

V. A. Liskovets and T. R. S. Walsh, Enumeration of Eulerian and unicursal planar maps, Discr. Math., 282 (2004), 209-221.

Mathematica

a[1] = a[2] = 1;
a[n_] := With[{m = Floor[(n+1)/2]}, 1/n 2^(n-3) Binomial[2n-2, n-1] + 2^(m-3) Binomial[2m-2, m-1]];
Array[a, 20] (* Jean-François Alcover, Aug 28 2019 *)

Crossrefs

Cf. A069727, A003645, A069732.

Sequence in context: A296321 A203768 A356268 * A291287 A193499 A261919

Adjacent sequences: A069722 A069723 A069724 * A069726 A069727 A069728

Keyword

easy,nonn

Author

Valery A. Liskovets, Apr 07 2002

Status

approved