0,2

Number of rooted 4-regular planar maps with n vertices.

Also, number of doodles with n crossings, irrespective of the number of loops.

R. Cori and B. Vauquelin, Planar maps are well labeled trees, Canad. J. Math., 33 (1981), 1023-1042.

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 714.

V. A. Liskovets, A census of nonisomorphic planar maps, in Algebraic Methods in Graph Theory, Vol. II, ed. L. Lovasz and V. T. Sos, North-Holland, 1981.

V. A. Liskovets, Enumeration of nonisomorphic planar maps, Selecta Math. Sovietica, 4 (No. 4, 1985), 303-323.

R. C. Mullin, On the average activity of a spanning tree of a rooted map, J. Combin. Theory, 3 (1967), 103-121.

W. T. Tutte, A census of planar maps, Canad. J. Math., 15 (1963), 249-271.

T. D. Noe, Table of n, a(n) for n=0..100

M. Bousquet-Melou, Limit laws for embedded trees

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

G. Schaeffer and P. Zinn-Justin, On the asymptotic number of plane curves and alternating knots

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 516

G.f. satisfies A(z) = 1 - 16z +18zA - 27z^2A^2.

G.f.: F(1/2,1;3;12x). [From Paul Barry (pbarry(AT)wit.ie), Feb 04 2009]

a(n)=2*3^n*A000108(n)/(n+2). [From Paul Barry (pbarry(AT)wit.ie), Feb 04 2009]

f:=n->2*3^n*(2*n)!/(n!*(n+2)!);

First row of array A102994. Cf. A005470.

Adjacent sequences: A000165 A000166 A000167 this_sequence A000169 A000170 A000171

Sequence in context: A074602 A073986 A089436 this_sequence A127128 A064151 A075679

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).