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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A270406 Triangle read by rows: T(n,g) is the number of rooted maps with n edges and 2 faces on an orientable surface of genus g. 6
1, 5, 22, 10, 93, 167, 386, 1720, 483, 1586, 14065, 15018, 6476, 100156, 258972, 56628, 26333, 649950, 3288327, 2668750, 106762, 3944928, 34374186, 66449432, 12317877, 431910, 22764165, 313530000, 1171704435, 792534015, 1744436, 126264820, 2583699888, 16476937840, 26225260226, 4304016990 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n contains floor((n+1)/2) terms.

LINKS

Gheorghe Coserea, Rows n = 1..101, flattened

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

EXAMPLE

Triangle starts:

n\g    [0]          [1]          [2]          [3]          [4]

[1]    1;

[2]    5;

[3]    22,          10;

[4]    93,          167;

[5]    386,         1720,        483;

[6]    1586,        14065,       15018;

[7]    6476,        100156,      258972,      56628;

[8]    26333,       649950,      3288327,     2668750;

[9]    106762,      3944928,     34374186,    66449432,    12317877;

[10]   431910,      22764165,    313530000,   1171704435,  792534015;

[11]   ...

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) ((2n-1)/3 Q[n-1, f, g] + (2n-1)/3 Q[n - 1, f-1, g] + (2n-3) (2n-2) (2n-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] (2k-1) (2l-1) Q[k-1, u, i] Q[l-1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);

Table[Table[Q[n, 2, g], {g, 0, (n+1)/2-1}], {n, 1, 11}] // Flatten (* Jean-Fran├žois Alcover, Aug 10 2018 *)

PROG

(PARI)

N = 10; F = 2; gmax(n) = n\2;

Q = matrix(N + 1, N + 1);

Qget(n, g) = { if (g < 0 || g > n/2, 0, Q[n+1, g+1]) };

Qset(n, g, v) = { Q[n+1, g+1] = v };

Quadric({x=1}) = {

  Qset(0, 0, x);

  for (n = 1, length(Q)-1, for (g = 0, gmax(n),

    my(t1 = (1+x)*(2*n-1)/3 * Qget(n-1, g),

       t2 = (2*n-3)*(2*n-2)*(2*n-1)/12 * Qget(n-2, g-1),

       t3 = 1/2 * sum(k = 1, n-1, sum(i = 0, g,

       (2*k-1) * (2*(n-k)-1) * Qget(k-1, i) * Qget(n-k-1, g-i))));

    Qset(n, g, (t1 + t2 + t3) * 6/(n+1))));

};

Quadric('x + O('x^(F+1)));

concat(vector(N+2-F, n, vector(1 + gmax(n-1), g, polcoeff(Qget(n+F-2, g-1), F))))

CROSSREFS

Columns k=0-1 give: A000346, A006295.

Sequence in context: A156860 A225846 A247937 * A209049 A217444 A063619

Adjacent sequences:  A270403 A270404 A270405 * A270407 A270408 A270409

KEYWORD

nonn,tabf

AUTHOR

Gheorghe Coserea, Mar 16 2016

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 January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)