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A003584 Unicursal (i.e., possessing an Eulerian path) planar rooted maps with n edges. 1
1, 2, 9, 52, 336, 2304, 16368, 118976, 878592, 6562816, 49447424, 375072768, 2860343296, 21909012480, 168425533440, 1298753372160, 10041201131520, 77809145610240, 604138825973760, 4698956908462080, 36604934482821120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

Table of n, a(n) for n=0..20.

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

FORMULA

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

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-Fran├žois Alcover, Dec 11 2014 *)

CROSSREFS

Cf. A000257, A005470, A069720.

Sequence in context: A009310 A091319 A193465 * A301928 A069271 A305987

Adjacent sequences:  A003581 A003582 A003583 * A003585 A003586 A003587

KEYWORD

nonn,nice

AUTHOR

Valery A. Liskovets

EXTENSIONS

More terms from Valery A. Liskovets, Apr 07 2002

STATUS

approved

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Last modified October 17 11:44 EDT 2019. Contains 328108 sequences. (Running on oeis4.)