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A006402 Number of sensed 2-connected (nonseparable) planar maps with n edges.
(Formerly M0812)
5
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 (list; graph; refs; listen; history; text; internal format)
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
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.
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(23) and beyond from Andrew Howroyd, Mar 29 2021
STATUS
approved

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)