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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). 2
1, 1, 3, 11, 62, 342, 2152, 13768, 91800, 622616, 4301792, 30100448, 213019072, 1521473984, 10954616064, 79420280064, 579300888960, 4248201302400, 31302536066560, 231638727063040 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Aug 28 2019 *)

CROSSREFS

Cf. A069727, A003645, A069732.

Sequence in context: A203007 A296321 A203768 * A291287 A193499 A261919

Adjacent sequences:  A069722 A069723 A069724 * A069726 A069727 A069728

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Apr 07 2002

STATUS

approved

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)