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.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

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

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

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.

Sequence in context: A074602 A073986 A089436 this_sequence A127128 A064151 A075679

Adjacent sequences: A000165 A000166 A000167 this_sequence A000169 A000170 A000171

nonn,nice,easy

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