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 A288084 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 2. 9
 66066, 3288327, 85421118, 1558792200, 22555934280, 276221817810, 2979641557620, 29079129795702, 261637840342860, 2200626948631386, 17486142956133684, 132344695964811720, 960323177351524512, 6716133365837116980, 45466867668336614472, 299027167905149145858, 1916387674555902480660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 7,1 LINKS Table of n, a(n) for n=7..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, 4, 2]; Table[a[n], {n, 7, 23}] (* Jean-François Alcover, Oct 18 2018 *) PROG (PARI) A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x); A288084_ser(N) = { my(y = A000108_ser(N+1)); 3*y*(y-1)^7*(9318*y^6 + 178328*y^5 + 177929*y^4 - 611583*y^3 + 195218*y^2 + 110388*y - 37576)/(y-2)^20; }; Vec(A288084_ser(17)) CROSSREFS Rooted maps of genus 2 with n edges and f faces for 1<=f<=10: A006298 f=1, A288082 f=2, A288083 f=3, this sequence, A288085 f=5, A288086 f=6, A288087 f=7, A288088 f=8, A288089 f=9, A288090 f=10. Column 4 of A269922, column 2 of A270408. Cf. A000108. Sequence in context: A043678 A032781 A170799 * A194430 A254192 A254185 Adjacent sequences: A288081 A288082 A288083 * A288085 A288086 A288087 KEYWORD nonn AUTHOR Gheorghe Coserea, Jun 05 2017 STATUS approved

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Last modified July 24 12:16 EDT 2024. Contains 374583 sequences. (Running on oeis4.)