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A270407 Triangle read by rows: T(n,g) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus g. 5
2, 22, 164, 70, 1030, 1720, 5868, 24164, 6468, 31388, 256116, 258972, 160648, 2278660, 5554188, 1169740, 795846, 17970784, 85421118, 66449432, 3845020, 129726760, 1059255456, 1955808460, 351683046, 18211380, 875029804, 11270290416, 40121261136, 26225260226 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Row n contains floor(n/2) terms.

LINKS

Gheorghe Coserea, Rows n = 2..102, 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]

[2]    2;

[3]    22;

[4]    164,         70;

[5]    1030,        1720;

[6]    5868,        24164,       6468;

[7]    31388,       256116,      258972;

[8]    160648,      2278660,     5554188,     1169740;

[9]    795846,      17970784,    85421118,    66449432;

[10]   3845020,     129726760,   1059255456,  1955808460,  351683046;

[11]   18211380,    875029804,   11270290416, 40121261136, 26225260226;

[12]   ...

PROG

(PARI)

N = 11; F = 3; 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: A000184, A006296.

Sequence in context: A091169 A279380 A230835 * A000184 A007613 A279801

Adjacent sequences:  A270404 A270405 A270406 * A270408 A270409 A270410

KEYWORD

nonn,tabf

AUTHOR

Gheorghe Coserea, Mar 16 2016

STATUS

approved

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Last modified February 19 13:25 EST 2018. Contains 299333 sequences. (Running on oeis4.)