A005645 -id:A005645 - cp's OEIS frontend

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

N. J. A. Sloane

nonn

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

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

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

Row sums of A342061.

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

\\ 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

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

A239893 Irregular triangle read by rows: T(n,k) is the number of sensed 3-connected planar maps with n >= 4 faces and k >= 4 vertices.

Original entry on oeis.org

1, 0, 1, 1, 0, 1, 3, 2, 2, 0, 0, 2, 11, 16, 10, 6, 0, 0, 2, 16, 69, 127, 128, 60, 17, 0, 0, 0, 10, 127, 541, 1188, 1441, 1032, 386, 73, 0, 0, 0, 6, 128, 1188, 5096, 11982, 17265, 15466, 8582, 2652, 389, 0, 0, 0, 0, 60, 1441, 11982, 50586, 127765, 206880, 222472, 158057, 71980, 18914, 2274

Offset: 4

N. J. A. Sloane, Apr 03 2014

T(n,k) is the number of polyhedra with n faces and k vertices up to orientation preserving isomorphisms. The number of edges is n+k-2. - Andrew Howroyd, Mar 27 2021

			Triangle begins:
1
0 1 1
0 1 3  2   2
0 0 2 11  16   10     6
0 0 2 16  69  127   128    60     17
0 0 0 10 127  541  1188  1441   1032    386     73
0 0 0  6 128 1188  5096 11982  17265  15466   8582   2652   389
0 0 0  0  60 1441 11982 50586 127765 206880 222472 158057 71980 18914 2274
...

Andrew Howroyd, Table of n, a(n) for n = 4..199 (rows 4..17)
Gunnar Brinkmann and Brendan McKay, Fast generation of planar graphs (expanded edition), Table 9-11.
Timothy R. Walsh, Efficient enumeration of sensed planar maps, Discrete Math. 293 (2005), no. 1-3, 263--289. MR2136069 (2006b:05062).
Timothy R. S. Walsh, Counting nonisomorphic three-connected planar maps, J. Combin. Theory Ser. B 32 (1982), no. 1, 33-44.

Row and column sums are A119501.
Main diagonal is A342057.
The unsensed version is A212438.
Cf. A005645 (by edges).

T(n,k) = T(k,n). - Andrew Howroyd, Mar 27 2021

Terms a(67) and beyond from Andrew Howroyd, Mar 27 2021

cp's OEIS Frontend

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

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