A006394
Number of sensed planar maps with n edges and without loops or parallel edges.
Original entry on oeis.org
1, 1, 1, 3, 5, 15, 52, 213, 1002, 5167, 27967, 158447, 926786
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A006391
Number of unsensed loopless planar maps with n edges.
Original entry on oeis.org
1, 1, 2, 5, 14, 45, 191, 871, 4682, 27336, 172706, 1150322, 7989004
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A103941
Number of unrooted loopless n-edge maps in the plane (planar with a distinguished outside face).
Original entry on oeis.org
1, 1, 2, 6, 22, 103, 614, 3872, 26414, 186988, 1367976, 10254326, 78461338, 610598818, 4821248244, 38546510368, 311560875422, 2542507084588, 20925300483992, 173530381632724, 1448900079476152, 12172334379246523, 102833593763830038, 873187910184763024, 7449120536014301138
Offset: 0
- V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
-
a[n_] := (1/(2n)) (Binomial[4n, n]/(3n+1) + Sum[Boole[0 < k < n] EulerPhi[ n/k] Binomial[4k, k], {k, Divisors[n]}] + q[n]);
q[n_] := If[EvenQ[n], 0, Binomial[2n, (n-1)/2]];
Array[a, 20] (* Jean-François Alcover, Sep 01 2019 *)
-
a(n) = {if(n==0, 1, (sumdiv(n, d, if(dAndrew Howroyd, Mar 28 2021
a(0)=1 prepended and terms a(21) and beyond from
Andrew Howroyd, Mar 28 2021
A103942
Number of unrooted n-edge isthmusless maps in the plane (planar with a distinguished outside face).
Original entry on oeis.org
1, 1, 3, 9, 38, 187, 1120, 7083, 47990, 337676, 2455517, 18310155, 139447034, 1080773098, 8502896424, 67763884363, 546147639926, 4445389286380, 36501274080076, 302060508150976, 2517213486505592, 21110062391001119, 178052027949519768, 1509631210682469661, 12860805940582898474
Offset: 0
- V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
-
a[n_] := (1/(2n)) ((5n^2 + 13n + 2) Binomial[4n, n]/((n+1)(3n+1)(3n+2)) + Sum[Boole[0 < k < n] EulerPhi[n/k] Binomial[4k, k], {k, Divisors[n]}] + q[n]);
q[n_] := If[EvenQ[n], 0, (n-1) Binomial[2n, (n-1)/2]]/(n+1);
Array[a, 20] (* Jean-François Alcover, Sep 01 2019 *)
-
a(n) = {if(n==0, 1, (sumdiv(n, d, if(dAndrew Howroyd, Mar 28 2021
a(0)=1 prepended and terms a(21) and beyond from
Andrew Howroyd, Mar 28 2021
A006398
Number of sensed planar maps with n edges and without loops or isthmuses.
Original entry on oeis.org
1, 0, 1, 2, 4, 8, 29, 92, 403, 1846, 9239, 48028, 259567
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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