login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A291371 Number of maximal chord diagrams of genus g counted up to rotations and reflections. 1
1, 4, 82, 7258, 1491629, 506855279, 254118439668, 176377605783906, 162019808170348933, 190375587419231088550, 278587959330563466969926, 496903413656110608290219603 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also the number of non-isomorphic one-face one-vertex maps on a genus g surface where both orientation-preserving and orientation-reversing isomorphisms are taken into account.

LINKS

Table of n, a(n) for n=1..12.

Evgeniy Krasko, Counting Unlabelled Chord Diagrams of Maximal Genus, arXiv:1709.00796 [math.CO], 2017.

Evgeny Krasko, A. Omelchenko, Enumeration of Chord Diagrams without Loops and Parallel Chords, arXiv preprint arXiv:1601.05073 [math.CO], 2016; Electronic Journal of Combinatorics 24(3) (2017), #P3.43

PROG

(Python 2.7)

rot_sym = [

  0, 1, 4, 131, 14118, 2976853, 1013582110, 508233789579, 352755124921122,

  324039613564554401, 380751174738424280720, 557175918657122229139987,

  993806827312044893602464496, # A291172

]

def u(n):

  if n < 0:

    return 0

  if n <= 1:

    return 1

  sum = 0

  sum -= (4 * n - 1) * u(n - 1)

  sum += n * (2 * n - 3) * (10 * n - 9) * u(n - 2)

  sum += 5 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * u(n - 3)

  sum -= 2 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * (2 * n - 6) * (2 * n - 7) * u(n - 4)

  return sum / (n + 1)

for i in range(1, 13):

  print (2 * rot_sym[i] + u(i) + u(i - 1) * (2 * i - 1)) / 4

CROSSREFS

Maximal diagrams up to rotations: A291172.

Sequence in context: A289224 A158981 A317889 * A007154 A056410 A056400

Adjacent sequences:  A291368 A291369 A291370 * A291372 A291373 A291374

KEYWORD

nonn

AUTHOR

Evgeniy Krasko, Sep 03 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 4 19:54 EDT 2020. Contains 336202 sequences. (Running on oeis4.)