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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 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-François 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 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.)