A006402 Number of sensed 2-connected (nonseparable) planar maps with n edges.

1, 2, 3, 6, 16, 42, 151, 596, 2605, 12098, 59166, 297684, 1538590, 8109078, 43476751, 236474942, 1302680941, 7256842362, 40832979283, 231838418310, 1327095781740, 7653155567834, 44434752082990, 259600430870176, 1525366978752096, 9010312253993072, 53485145730576790

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Some people begin this 2,1,2,3,6,..., others begin it 0,1,2,3,6,....

The dual of a nonseparable map is nonseparable, so the class of all nonseparable planar maps is self-dual. The maps considered here are unrooted and sensed and may include loops and parallel edges. - Andrew Howroyd, Mar 29 2021

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• T. R. S. Walsh, personal communication.

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..500
• V. A. Liskovets, T. R. S. Walsh, The enumeration of nonisomorphic 2-connected planar maps, Canad. J. Math. 35 (1983), no. 3, 417-435.
• Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.
• T. R. S. Walsh, Number of sensed planar maps with n edges and m vertices

Crossrefs

Row sums of A342061.

Cf. A000087 (with distinguished faces), A000139 (rooted), A005645, A006403 (unsensed), A006406 (without loops or parallel edges).

Programs

PARI

\\ here r(n) is A000139(n-1).
r(n)={4*binomial(3*n,n)/(3*(3*n-2)*(3*n-1))}
a(n)={(r(n) + sumdiv(n, d, if(dAndrew Howroyd, Mar 29 2021

Extensions

Terms a(23) and beyond from Andrew Howroyd, Mar 29 2021