A006402 Number of sensed 2-connected (nonseparable) planar maps with n edges. (Formerly M0812)

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

2,2

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

Prog

(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(d<n, eulerphi(n/d)*binomial(3*d-1, 2)*r(d))))/(2*n) + if(n%2, (n+1)*r((n+1)/2)/4, (3*n-4)*r(n/2)/16)} \\ Andrew Howroyd, Mar 29 2021

Crossrefs

Row sums of A342061.

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

Sequence in context: A159341 A159342 A089872 * A284417 A219024 A145860

Adjacent sequences: A006399 A006400 A006401 * A006403 A006404 A006405

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved