A006391 -id:A006391 - cp's OEIS frontend

A006390 Number of sensed loopless planar maps with n edges.

1, 1, 2, 5, 14, 49, 240, 1259, 7570, 47996, 319518, 2199295, 15571610, 112773478, 832809504, 6253673323, 47650870538, 367784975116, 2871331929096, 22647192990256, 180277915464664, 1447060793168493, 11703567787559680, 95312765368320637, 781151020141584190

Offset: 0

N. J. A. Sloane

nonn

By duality, also the number of sensed isthmusless planar maps with n edges. An isthmus may also be called a bridge. - Andrew Howroyd, Mar 28 2021

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

Andrew Howroyd, Table of n, a(n) for n = 0..500
V. A. Liskovets and T. R. S. Walsh, Counting Unrooted Loopless Planar Maps [Extended abstract]
V. A. Liskovets and T. R. S. Walsh, Counting unrooted loopless planar maps, Europ. J. Combin., 26:5 (2005), 651-663.
Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Cf. A000010, A006384, A000260 (rooted), A006391 (unsensed case), A103941 (with distinguished face), A103942 (with distinguished vertex).

a[n_] := If[n==0, 1, (1/(2n))(Sum[Binomial[4k, k] EulerPhi[n/k] Boole[ 0Jean-François Alcover, Aug 29 2019 *)

a(n) = {if(n==0, 1, (sumdiv(n, d, if(dAndrew Howroyd, Mar 28 2021

a(n) = (1/(2n))*[2(4n+1)*binomial(4n, n)/((n+1)*(3n+1)*(3n+2)) + Sum_{0A000010), q(n)=binomial(2n, (n-2)/2) if n is even and q(n)=2n*binomial(2n, (n-1)/2)/(n+1) if n is odd.

More terms from Valery A. Liskovets, Dec 01 2003

a(17) and a(19) corrected by Sean A. Irvine, Mar 26 2017

A006395 Number of unsensed planar maps with n edges and without loops or parallel edges.

Original entry on oeis.org

1, 1, 1, 3, 5, 14, 42, 150, 624, 2947, 15079, 82607, 474030, 2816952, 17194524, 107226255

Offset: 0

N. J. A. Sloane

The planar maps considered here are connected. A planar map without loops or parallel edges is called simple.

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

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Row sums of A384850, antidiagonal sums of A384963.

Cf. A006385, A006391, A006394 (sensed), A022558 (rooted), A372892 (with n vertices).

a(9)-a(12) from Sean A. Irvine, Mar 30 2017
a(0)=1 prepended by Andrew Howroyd, Jan 16 2025
a(13)-a(15) added by Andrew Howroyd, Jun 15 2025

A006399 Number of unsensed planar maps with n edges and without loops or isthmuses.

Original entry on oeis.org

1, 0, 1, 2, 4, 8, 27, 76, 295, 1188, 5462, 26580, 138110

Offset: 0

N. J. A. Sloane

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

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Cf. A006385, A006391, A006398 (sensed), A099553 (rooted).

a(9)-a(12) from Sean A. Irvine, Mar 29 2017

a(0)-a(1) prepended by Andrew Howroyd, Jan 16 2025

cp's OEIS Frontend

A006390 Number of sensed loopless planar maps with n edges.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A006395 Number of unsensed planar maps with n edges and without loops or parallel edges.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Extensions

A006399 Number of unsensed planar maps with n edges and without loops or isthmuses.

Views

Author

Keywords

References

Links

Crossrefs

Extensions