0,3

a(n)=3^(n-1)*S'(n+1) where S'(n) denotes the number of rooted non-separable planar maps with n edges (the sequence A006402).

Also counts rooted planar 3-constellations with n triangles: rooted planar maps with bicolored faces having n black triangular faces and an arbitrary number of white faces of degrees multiple to 3. - Valery Liskovets (liskov(AT)im.bas-net.by), Dec 01 2003

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

V. A. Kazakov, M. Staudacher and Th. Wynter, Character expansion methods for matrix models of dually weighted graphs, Commun. Math. Phys. 177 (1996), 451-468.

M. Bousquet-Melou and G. Schaeffer, Enumeration of planar constellations, Adv. in Appl. Math. v.24 (2000), 337-368.

M. Bousqet-Melou and A. Jehanne, Polynomial equations with one catalytic variable, algebraic series and map enumeration

a(n)=3^(n-1)*binomial(3n, n+1)/[n(2n+1)] G.f.: f(x)=(1+3y-y^2)/3 where 3x^2y^3-y+1=0.

G.f. satisfies A(z) = 1-47z+3z^2+3z(22-9z)A+9z(9z-2)A^2-81z^2A^3.

Cf. A000257, A006402.

Cf. A090372.

Sequence in context: A092472 A098658 A109576 this_sequence A081132 A158831 A034001

Adjacent sequences: A069723 A069724 A069725 this_sequence A069727 A069728 A069729

easy,nice,nonn

Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002