A214337 -id:A214337 - cp's OEIS frontend

A214806 Triangle read by rows: T(n,k) = number of rooted maps with n vertices and k faces on a non-orientable surface of type 2 (0 <= k <= n).

0, 0, 488, 0, 11660, 375552, 0, 160680, 6652366, 146387872, 0, 1678880, 86303920, 2298445830, 42795288180, 0, 14771680, 918342738, 28995928200, 629732269188, 10663498973088

Offset: 0

N. J. A. Sloane, Jul 28 2012

			Triangle begins:
  0,
  0,488,
  0,11660,375552,
  0,160680,6652366,146387872,
  0,1678880,86303920,2298445830,42795288180,
  0,14771680,918342738,28995928200,629732269188,10663498973088,
  ...

Didier Arquès and Alain Giorgetti, Counting rooted maps on a surface, Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078).

Diagonals give A118449, A214804, A214805, A214807. Cf. A214337.

A118448 Number of rooted n-edge one-vertex maps on a non-orientable genus-3 surface (dually: one-face maps).

Original entry on oeis.org

41, 690, 7150, 58760, 420182, 2736524, 16661580, 96411060, 536075430, 2886649260, 15139322276, 77665981120, 391031449340, 1937266785080, 9464122525784, 45670084085004, 218002466412870, 1030588793671980

Offset: 3

Valery A. Liskovets, May 04 2006

nonn

One-vertex maps on the Klein bottle are counted by A118447 and one-vertex maps on a non-orientable genus-4 surface by A118449. Such maps are also called bouquets of loops (and their duals are called unicellular maps).

E. R. Canfield, Calculating the number of rooted maps on a surface, Congr. Numerantium, 76 (1990), 21-34.
D. M. Jackson and T. I. Visentin, An atlas of the smaller maps in orientable and nonorientable surfaces. CRC Press, Boca Raton, 2001.

R. J. Mathar, Table of n, a(n) for n = 3..100
Didier Arquès, Alain Giorgetti, Counting rooted maps on a surface, Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078). - _N. J. A. Sloane_, Jul 27 2012

A diagonal of A214337.

((R-1)^3 (R+1)^2 (11 R^2 - 29 R - 64)/(64 R^8) /. R -> Sqrt[1-4x]) + O[x]^21 // CoefficientList[#, x]& // Drop[#, 3]& (* Jean-François Alcover, Aug 29 2019 *)

O.g.f.: (R-1)^3*(R+1)^2*(11*R^2-29*R-64)/(64*R^8), where R=sqrt(1-4*x).
D-finite with recurrence (69104*n+95905)*(n-2)*(n-3) *a(n) +2*(n-3) *(34552*n^2-2691825*n+3948578) *a(n-1) +4*(-967456*n^3+10134720*n^2-23520179*n+15213000) *a(n-2) + 144 *(2*n-5) *(34552*n-41477) *(n-2) *a(n-3)=0. R. J. Mathar, Oct 17 2012
a(n) ~ n^3 * 2^(2*n-1) / 3 * (1 - 7/(4*sqrt(Pi*n))). - Vaclav Kotesovec, Oct 27 2024

A214335 Number of rooted maps with n vertices and 2 faces on a non-orientable surface of type 3/2.

Original entry on oeis.org

0, 690, 16925, 237652, 2518957, 22417804

Offset: 0

N. J. A. Sloane, Jul 27 2012

nonn

Didier Arquès and Alain Giorgetti, Counting rooted maps on a surface, Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078).

A diagonal of A214337.

A214336 Number of rooted maps with n vertices and 3 faces on a non-orientable surface of type 3/2.

Original entry on oeis.org

0, 7150, 237652, 4306778, 56864524, 613687758

Offset: 0

N. J. A. Sloane, Jul 27 2012

Didier Arquès and Alain Giorgetti, Counting rooted maps on a surface, Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078).

A diagonal of A214337.

A214338 Number of rooted maps with n vertices and n faces on a non-orientable surface of type 3/2.

Original entry on oeis.org

0, 41, 16925, 4306778, 910734615, 174833737848

Offset: 0

N. J. A. Sloane, Jul 27 2012

Didier Arquès and Alain Giorgetti, Counting rooted maps on a surface, Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078).

A diagonal of A214337.

cp's OEIS Frontend

A214806 Triangle read by rows: T(n,k) = number of rooted maps with n vertices and k faces on a non-orientable surface of type 2 (0 <= k <= n).

Views

Author

Keywords

Examples

Links

Crossrefs

A118448 Number of rooted n-edge one-vertex maps on a non-orientable genus-3 surface (dually: one-face maps).

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

Formula

A214335 Number of rooted maps with n vertices and 2 faces on a non-orientable surface of type 3/2.

Views

Author

Keywords

Links

Crossrefs

A214336 Number of rooted maps with n vertices and 3 faces on a non-orientable surface of type 3/2.

Views

Author

Keywords

Links

Crossrefs

A214338 Number of rooted maps with n vertices and n faces on a non-orientable surface of type 3/2.

Views

Author

Keywords

Links

Crossrefs