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 A288083 a(n) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus 2. 9
 6468, 258972, 5554188, 85421118, 1059255456, 11270290416, 106853266632, 925572602058, 7454157823560, 56532447160536, 407653880116680, 2815913391715452, 18743188498056288, 120789163612555200, 756589971284883792, 4621041111902656770, 27595482540212519064, 161490751719681569736 (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, 3, 2]; Table[a[n], {n, 6, 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); A288083_ser(N) = { my(y = A000108_ser(N+1)); -6*y*(y-1)^6*(161*y^5 + 4005*y^4 + 4173*y^3 - 10701*y^2 + 2880*y + 560)/(y-2)^17; }; Vec(A288083_ser(18)) CROSSREFS Rooted maps of genus 2 with n edges and f faces for 1<=f<=10: A006298 f=1, A288082 f=2, this sequence, A288084 f=4, A288085 f=5, A288086 f=6, A288087 f=7, A288088 f=8, A288089 f=9, A288090 f=10. Column 3 of A269922, column 2 of A270407. Cf. A000108. Sequence in context: A067928 A166223 A206538 * A232134 A318629 A213117 Adjacent sequences: A288080 A288081 A288082 * A288084 A288085 A288086 KEYWORD nonn AUTHOR Gheorghe Coserea, Jun 05 2017 STATUS approved

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Last modified May 19 11:36 EDT 2024. Contains 372683 sequences. (Running on oeis4.)