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!)
A288072 a(n) is the number of rooted maps with n edges and 5 faces on an orientable surface of genus 1. 9
2310, 100156, 2278660, 36703824, 472592916, 5188948072, 50534154408, 448035881592, 3682811916980, 28442316247080, 208462422428152, 1461307573813824, 9857665477085832, 64309102366765200, 407372683115470800, 2514120288996270024, 15159074541052024308, 89512241718624419624 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

LINKS

Table of n, a(n) for n=6..23.

Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

MATHEMATICA

Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;

Q[n_, f_, g_] := Q[n, f, g] = 6/(n + 1) ((2 n - 1)/3 Q[n - 1, f, g] + (2 n - 1)/3 Q[n - 1, f - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 Q[n - 2, f, g - 1] + 1/2 Sum[l = n - k; Sum[v = f - u; Sum[j = g - i; Boole[l >= 1 && v >= 1 && j >= 0] (2 k - 1) (2 l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);

a[n_] := Q[n, 5, 1];

Table[a[n], {n, 6, 23}] (* Jean-Fran├žois Alcover, Oct 18 2018 *)

PROG

(PARI)

A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);

A288072_ser(N) = {

  my(y = A000108_ser(N+1));

  -2*y*(y-1)^6*(2140*y^5 + 14751*y^4 - 15604*y^3 - 8820*y^2 + 10176*y - 1488)/(y-2)^17;

};

Vec(A288072_ser(18))

CROSSREFS

Rooted maps of genus 1 with n edges and f faces for 1<=f<=10: A002802(with offset 2) f=1, A006295 f=2, A006296 f=3, A288071 f=4, this sequence, A287046 f=6, A287047 f=7, A287048 f=8, A288073 f=9, A288074 f=10.

Column 5 of A269921.

Cf. A000108.

Sequence in context: A147572 A046303 A046403 * A087978 A261210 A020435

Adjacent sequences:  A288069 A288070 A288071 * A288073 A288074 A288075

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Jun 05 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 February 20 16:42 EST 2020. Contains 332080 sequences. (Running on oeis4.)