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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]   ... 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}]); T[n_, g_] := Q[n, 3, g]; Table[T[n, g], {n, 2, 11}, {g, 0, Quotient[n, 2]-1}] // Flatten (* Jean-François Alcover, Oct 18 2018 *) 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 January 19 16:10 EST 2019. Contains 319307 sequences. (Running on oeis4.)