A003584 Unicursal (i.e., possessing an Eulerian path) planar rooted maps with n edges.

1, 2, 9, 52, 336, 2304, 16368, 118976, 878592, 6562816, 49447424, 375072768, 2860343296, 21909012480, 168425533440, 1298753372160, 10041201131520, 77809145610240, 604138825973760, 4698956908462080, 36604934482821120

Offset: 0

Author

Valery A. Liskovets

Keywords

• nonn
• nice

Comments

Unicursal (in a broad sense) means that no more than two vertices are of odd valency (that is maps possessing an Eulerian path or cycle).

Links

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

Crossrefs

Cf. A000257, A005470, A069720.

Programs

Mathematica

a[n_] := 2^(n-1)*(3*Binomial[2*n, n]/((n+1)*(n+2))+Binomial[2*n-1, n]); a[0]=1; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Dec 11 2014 *)

Formula

a(n) = A000257(n) + A069720(n).

Extensions

More terms from Valery A. Liskovets, Apr 07 2002